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Journal articles on the topic 'Bitopological space'

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Published: 3 June 2025
Last updated: 31 July 2025

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1

Arunmaran, M., та K. Kannan. "Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces". Journal of Mathematics 2018 (2018): 1–4. http://dx.doi.org/10.1155/2018/7863713.

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We are going to establish some results of τ1τ2-δ semiconnectedness and compactness in a bitopological space. Besides, we will investigate several results in τ1τ2-δ semiconnectedness for subsets in bitopological spaces. In particular, we will discuss the relationship related to semiconnectedness between the topological spaces and bitopological space. That is, if a bitopological space (X,τ1,τ2) is τ1τ2-δ semiconnected, then the topological spaces (X,τ1) and (X,τ2) are δ-semiconnected. In addition, we introduce the result which states that a bitopological space (X,τ1,τ2) is τ1τ2-δ semiconnected i
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2

Al-Abayechi, Ameer, Haneen Al-Janabi, and Heyam Kh Hassan Alkhayyat. "New results in fuzzy soft bitopological spaces via (1,2)-fuzzy soft preopen sets." Journal of Interdisciplinary Mathematics 28, no. 3-B (2025): 1161–72. https://doi.org/10.47974/jim-2205.

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Makherjee and Park [1] introduced and studied a notion for a fuzzy soft bitopological space. This article introduce notions for fuzzy soft pre-open (closed) set of fuzzy soft bitopological space and studied their basic properties. we use these notions to characterize fundamental concepts of fuzzy soft bitopological spaces such as fuzzy soft pre-closures and fuzzy soft pre-interior of a fuzzy soft bitopological space and prove some of their axioms. Through the use of a notion for soft quasi coincidence, as well as we characterized the concept for a fuzzy soft quasi pre-separation axioms of bito
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3

Mehmood, Arif, Mohammed M. Al-Shomrani, Muhammad Asad Zaighum, and Saleem Abdullah. "Characterization of Soft S-Open Sets in Bi-Soft Topological Structure Concerning Crisp Points." Mathematics 8, no. 12 (2020): 2100. http://dx.doi.org/10.3390/math8122100.

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In this article, a soft s-open set in soft bitopological structures is introduced. With the help of this newly defined soft s-open set, soft separation axioms are regenerated in soft bitopological structures with respect to crisp points. Soft continuity at some certain points, soft bases, soft subbase, soft homeomorphism, soft first-countable and soft second-countable, soft connected, soft disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. The product of two soft axioms with respect crisp points with almost al
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4

Hassan, Ameer Mohammad-Husain. "Pre-Open Sets In Minimal Bitopological Spaces." Journal of Kufa for Mathematics and Computer 2, no. 3 (2015): 27–43. http://dx.doi.org/10.31642/jokmc/2018/020303.

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Let be a topological space, let be an M-structure on then is called a minimal bitopological space. In this work, I am study pre-open sets in minimal bitopological spaces with some result and definitions separation axioms on minimal bitopological with study some fundamental of their properties.
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Tripathy, Binod Chandra, and Shyamal Debnath. "Fuzzy $m$-structures $m$-open multifunctions and bitopological spaces." Boletim da Sociedade Paranaense de Matemática 37, no. 4 (2018): 119–28. http://dx.doi.org/10.5269/bspm.v37i4.35152.

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In this paper we study different weak forms of open multifunctionsfrom a fuzzy topological space into a fuzzy $m$-space. Further we study the same from a fuzzy bitopological space into a fuzzy bitopological spaces.
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6

Qoqazeh, Hamza, Ali Atoom, Maryam Alholi, et al. "$ KC $-bitopological spaces." AIMS Mathematics 9, no. 11 (2024): 32182–99. http://dx.doi.org/10.3934/math.20241545.

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<p>A topological space $ \left(X, \tau \right) $ is called a $ KC $-space when every compact subset of $ X $ is closed. The aim of this paper is to introduce new, namely $ KC $-bitopological spaces and pairwise $ KC $-topological spaces "$ P $-$ KC $-topological spaces". We examined the properties of these concepts and showed the relationships between these concepts and other bitopological spaces. We also discussed the effect of some types of functions on $ KC $-bitopological spaces and pairwise $ KC $-topological spaces. Several examples are discussed, and many well-known theories are g
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7

Thangaraj, G., and V. Chandiran. "Estimating Pairwise Fuzzy Spaces using Residual Sets Spaces." International Journal of Engineering and Advanced Technology 9, no. 1s5 (2019): 199–203. http://dx.doi.org/10.35940/ijeat.a1051.1291s519.

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The main focus of this paper is to introduce the new types of pairwise fuzzy Volterra spaces such as by introducing pairwise fuzzy residual sets in the place of pairwise fuzzy Gδ-sets in the definition of pairwise fuzzy Volterra space, a new kind of fuzzy bitopological space namely, pairwise fuzzy εr-Volterra spaces has been introduced and studied and also by introducing pairwise fuzzy pre-open sets in the place of pairwise fuzzy dense sets in the definition of pairwise fuzzy Volterra space, another kind of fuzzy bitopological space namely, pairwise fuzzy εr-Volterra spaces has been introduced
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8

Sarma, Diganta Jyoti, and Binod Chandra Tripathy. "Pairwise Generalized b-Ro Spaces in Bitopological Spaces." Proyecciones (Antofagasta) 36, no. 4 (2018): 589–600. https://doi.org/10.22199/issn.0717-6279-2537.

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The main purpose of this paper is to introduce pairwise generalized b-Ro spaces in bitopological spaces with the help of generalized b-open sets in bitopological spaces and give several characterizations of this spaces. We also introduce generalized b-kernel of a set and investigate some properties of it and study the relationship between this space and other bitopological spaces.
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9

Shalil,, S. H., S. A. El-Sheikh,, and S. A. Kandil,. "On Soft Bitopological Ordered Spaces." Malaysian Journal of Mathematical Sciences 18, no. 1 (2024): 9–38. http://dx.doi.org/10.47836/mjms.18.1.02.

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This paper introduces soft bitopological ordered spaces, combining soft topological spaces with partial order relations. The authors extensively investigate increasing, decreasing, and balancing pairwise open and closed soft sets, analyzing their properties. They prove that the collection of increasing (decreasing) open soft sets forms an increasing (decreasing) soft topology. The paper thoroughly examines increasing and decreasing pairwise soft closure and interior operators. Notably, it introduces bi−ordered soft separation axioms, denoted as PSTi(PST∙i,PST∗i,PST∗∗i)− ordered spaces, i=0,1,2
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10

Ghour, Samer Al, and Almothana Azaizeh. "Fuzzy Homogeneous Bitopological Spaces." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 6 (2018): 4619. http://dx.doi.org/10.11591/ijece.v8i6.pp4619-4625.

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We continue the study of the concepts of minimality and homogeneity in the fuzzy context. Concretely, we introduce two new notions of minimality in fuzzy bitopological spaces which are called minimal fuzzy open set and pairwise minimal fuzzy open set. Several relationships between such notions and a known one are given. Also, we provide results about the transformation of minimal, and pairwise minimal fuzzy open sets of a fuzzy bitopological space, via fuzzy continuous and fuzzy open mappings, and pairwise continuous and pairwise open mappings, respectively. Moreover, we present two new notion
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11

Al, Ghour Samer, and Almothana Azaizeh. "Fuzzy Homogeneous Bitopological Spaces." International Journal of Electrical and Computer Engineering (IJECE) 8, no. 6 (2018): 4619–25. https://doi.org/10.11591/ijece.v8i6.pp4619-4625.

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We continue the study of the concepts of minimality and homogeneity in the fuzzy context. Concretely, we introduce two new notions of minimality in fuzzy bitopological spaces which are called minimal fuzzy open set and pairwise minimal fuzzy open set. Several relationships between such notions and a known one are given. Also, we provide results about the transformation of minimal, and pairwise minimal fuzzy open sets of a fuzzy bitopological space, via fuzzy continuous and fuzzy open mappings, and pairwise continuous and pairwise open mappings, respectively. Moreover, we present two new notion
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12

Oudetallah, Jamal, Rehab Alharbi, and Iqbal M. Batiha. "On r-Compactness in Topological and Bitopological Spaces." Axioms 12, no. 2 (2023): 210. http://dx.doi.org/10.3390/axioms12020210.

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This paper defines the so-called pairwise r-compactness in topological and bitopological spaces. In particular, several inferred properties of the r-compact spaces and their connections with other topological and bitopological spaces are studied theoretically. As a result, several novel theorems of the r-compact space are generalized on the pairwise r-compact space. The results established in this research paper are new in the field of topology.
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13

Acharjee, Santanu, Kyriakos Papadopoulos, and Binod Chandra Tripathy. "Note on $p_1$-Lindelof spaces which are not contra second countable spaces in bitopology." Boletim da Sociedade Paranaense de Matemática 38, no. 1 (2018): 165–71. http://dx.doi.org/10.5269/bspm.v38i1.34701.

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In this article we show that a contra second countable bitopological space is a $p_1$-Lindelof space, but the converse is not true in general. We provide suitable example with the help of concepts of nest and interlocking from LOTS. The relation between pairwise regular spaces and $p_1$-normal spaces is studied. At the end, we propose some open questions which may enrich various concepts related to Lindelofness in a bitopological space and other areas of mathematical ideas.
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14

Miah, Saikh Shahjahan, Ranapati Ronjon, and Nigar Sultana. "An in-depth exploration of intuitionistic fuzzy T_0 in the context of bitopology." Notes on Intuitionistic Fuzzy Sets 30, no. 1 (2024): 66–76. http://dx.doi.org/10.7546/nifs.2024.30.1.66-76.

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Intuitionistic fuzzy topological space and bitopological space have been introduced by using the concepts of intuitionistic fuzzy sets which are the generalizations of interval valued fuzzy sets. This paper commences by presenting the notion of intuitionistic fuzzy T0 in the context of bitopological spaces (IFB-T0). Subsequently, we explore various connections and relationships between these concepts. Then, we find out the relation between intuitionistic T0 and IFB-T0 spaces. Further, we investigated continuity between two IFB spaces.
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15

Chentsov, A. G. "Superextension as bitopological space." Izvestiya Instituta Matematiki i Informatiki. Udmurt. Gos. Univ. 49 (May 2017): 55–79. http://dx.doi.org/10.20537/2226-3594-2017-49-03.

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16

Tutanes, Lezel Mernilo. "On $\psi$ gs-Functions in Bitopological Spaces." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 2173–81. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5208.

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A subset $A$ of a bitopological space $(X,\tau_1,\tau_2)$ is called \emph{$(i,j)$-$\psi$gs-closed} set if\\ $(i,j)\text{-}\psi cl(A)\subseteq U$ whenever $A\subseteq U$, $U$ is $(i,j)$-semi-open in $(X,\tau_1,\tau_2)$. In this work, the propertiesof this set are considered to investigate the concepts of $\psi gs$-functions in bitopological spaces. Specifically, this study establishes some properties and provide characterizations of $\psi gs$-open and $\psi gs$-closed functions, $\psi gs$-continuous functions, and $\psi gs$-irresolute functions in bitopological spaces.
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17

Raghavan, T. G., and I. L. Reilly. "A new bitopological paracompactness." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 2 (1986): 268–74. http://dx.doi.org/10.1017/s144678870003367x.

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AbstractIn this paper we define generalization of paracompactness for bitopological spaces. (X, τ1, τ2) is Δ-pairwise paracompact if and only if every τi open cover admits a τ1 ∨ τ2 open refinement which is τ1 ∨ τ2 locally finite. Every quasimetric space (X, τp, τq) is Δ-pairwise paracompact. An analogue of Michael's characterization of regular paracompact spaces is proved for Δ-pairwise paracompact spaces.
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18

Ogola, O., N. B. Okelo, and O. Ongati. "On separability criteria for continuous Bitopological spaces." Open Journal of Mathematical Analysis 5, no. 2 (2021): 31–45. http://dx.doi.org/10.30538/psrp-oma2021.0091.

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In this paper, we give characterizations of separation criteria for bitopological spaces via \(ij\)-continuity. We show that if a bitopological space is a separation axiom space, then that separation axiom space exhibits both topological and heredity properties. For instance, let \((X, \tau_{1}, \tau_{2})\) be a \(T_{0}\) space then, the property of \(T_{0}\) is topological and hereditary. Similarly, when \((X, \tau_{1}, \tau_{2})\) is a \(T_{1}\) space then the property of \(T_{1}\) is topological and hereditary. Next, we show that separation axiom \(T_{0}\) implies separation axiom \(T_{1}\)
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19

Thamilisai, A., and S. Brindha. "T (1,2)*-SPACES." International Journal of Emerging Research in Management and Technology 6, no. 6 (2018): 140. http://dx.doi.org/10.23956/ijermt.v6i6.259.

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In this paper we discussed about A bitopological space X is called an gT (1,2)*-space if every (1,2)*-g-closed set in it is (1,2)*-closed. And A bitopological space X is called a T (1,2)*-space if every (1,2)*-closed subset of X is τ1,2-closed in X. and we are also going to prove that Every (1,2)*-αTb-space is T (1,2)*-space but not conversely
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20

Alharbi, Rehab, Jamal Oudetallah, Mutaz Shatnawi, and Iqbal M. Batiha. "On c-Compactness in Topological and Bitopological Spaces." Mathematics 11, no. 20 (2023): 4251. http://dx.doi.org/10.3390/math11204251.

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The primary goal of this research is to initiate the pairwise c-compact concept in topological and bitopological spaces. This would make us to define the concept of c-compact space with some of its generalization, and present some necessary notions such as the H-closed, the quasi compact and extremely disconnected compact spaces in topological and bitopological spaces. As a consequence, we derive numerous theoretical results that demonstrate the relations between c-separation axioms and the c-compact spaces.
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21

Acharjee, Santanu, and B. C. Tripathy. "$p$-$\mathcal{I}$-generator and $p_1$-$\mathcal{i}$-generator in bitopology." Boletim da Sociedade Paranaense de Matemática 36, no. 2 (2018): 17–31. http://dx.doi.org/10.5269/bspm.v36i2.29377.

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In this article we have investigated the relations of $p$-$\mathcal{I}$-generator, $p_1$-$\mathcal{I}$-generator with $p$-Lindel\"{o}f and $p_1$-Lindel\"{o}f using $\tau_i$-codense, $(i,j)$-meager, $(i,j)$-nowhere dense and perfect mapping of bitopological space. The relations between $p$-compactness, $p$-Lindel\"{o}fness, $p_1$-Lindel\"{o}fness and topological ideal, $(i,j)$-meager, $(i,j)$-Baire space in bitopological space are investigated. Some properties are studied on product bitopology using perfect mapping. It can be found that bitopological space has many applications in real life pro
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22

Al Ghour, Samer. "Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts." Mathematics 9, no. 15 (2021): 1781. http://dx.doi.org/10.3390/math9151781.

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In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respective
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23

Şenel, Güzide. "A New Approach to Hausdorff Space Theory via the Soft Sets." Mathematical Problems in Engineering 2016 (2016): 1–6. http://dx.doi.org/10.1155/2016/2196743.

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The aim of this paper is to present the concept of soft bitopological Hausdorff space (SBT Hausdorff space) as an original study. Firstly, I introduce some new concepts in soft bitopological space such as SBT point, SBT continuous function, and SBT homeomorphism. Secondly, I define SBT Hausdorff space. I analyse whether a SBT space is Hausdorff or not by SBT homeomorphism defined from a SBT Hausdorff space to researched SBT space. I end my study by defining SBT property and hereditary SBT by SBT homeomorphism and investigate the relations between SBT space and SBT subspace.
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24

Hossain, MS, and Ummey Habiba. "Level Separation on Fuzzy Pairwise T0bitopological Space." Journal of Bangladesh Academy of Sciences 41, no. 1 (2017): 57–68. http://dx.doi.org/10.3329/jbas.v41i1.33504.

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In this paper, we introduce five notions of level separation in T0 fuzzy bitopological spaces. We establish some relation among them. Also, we find relations between fuzzy topological spaces and corresponding fuzzy bitopological spaces in such spaces. Further, we prove that all these definitions satisfy “good extension” property. Finally, we prove that all these notionsare hereditary, productive and projective, moreover we observe that all concepts are preserved under one-one, onto and continuous mapping.Journal of Bangladesh Academy of Sciences, Vol. 41, No. 1, 57-68, 2017
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25

Venkatesh, K. A., and S. Balasubramanian. "Weak and Strong Bitopological Lindel of Space." Mapana - Journal of Sciences 1, no. 2 (2003): 12–14. http://dx.doi.org/10.12723/mjs.2.3.

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26

Miah, Saikh Shahjahan Miah, and M. R. Amin. "Normal Separation Axiom on Fuzzy Bitopological Space." MBSTU Journal of Science and Technology 9, no. 1 and 2 (2023): 21–24. http://dx.doi.org/10.69728/jst.v9.18.

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In our paper, we present three novel concepts related to the normal separation property within the realm of fuzzy bitopological spaces (FPTS), specifically focusing on pairwise fuzzy normal bitopological spaces (FPN). These notions are introduced in a quasi-coincidence sense, and we establish relationships between our propositions and other existing ones. Furthermore, we provide proofs demonstrating that all the introduced concepts exhibit the ‘good extension’ property. Notably, we observe that our notions maintain their characteristics under one-one, onto, fuzzy pairwise open (FP-open), fuzzy
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27

Kovár, Martin M. "A note on the comparison of topologies." International Journal of Mathematics and Mathematical Sciences 26, no. 4 (2001): 233–37. http://dx.doi.org/10.1155/s0161171201005518.

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A considerable problem of some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is RR-pairwise paracompact, its two topologies will collapse and revert to the unitopological case. We introduce a new bitopological separation axiomτS2σwhich is appropriate for the study of the bitopological collapse. We also show that the property that may cause the collapse is much weaker than some modifications of pairwise paracompactness and we generalize several results of T. G. Raghavan and I
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28

Omer, N. M., H. Z. Hdeib, E. M. Almuhur, and M. Al-Labadi. "ON P_2-C-CLOSED SPACE IN BITOPOLOGICAL SPACE." Advances in Mathematics: Scientific Journal 10, no. 3 (2021): 1839–43. http://dx.doi.org/10.37418/amsj.10.3.61.

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29

Emwas, J. A., and H. Z. Hdeib. "COMPACT COMPLEMENT TOPOLOGIES IN BITOPOLOGICAL SPACE." Advances in Mathematics: Scientific Journal 10, no. 4 (2021): 2181–85. http://dx.doi.org/10.37418/amsj.10.4.32.

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Let $(X, \tau_{0}, \tau_{1})$ be a Hausdorff space, where $X$ is an infinite set. The compact complement topologies in bitopological space $(X, \tau_{0}, \tau_{1})$ are $\tau_{0}^*$ and $\tau_{1}^*$ where $\tau_{0}^*$ = $\{\emptyset\}$ $\cup$ $\{X \setminus M_{0} : M_{0}$ is $\tau_{0}$-compact\} and $\tau_{1}^*$ = $\{\emptyset\}$ $\cup$ $\{X \setminus M_{1} : M_{1}$ is $\tau_{1}$-compact\}. Throughout this paper, some properties of the space $(X, \tau_{0}^*, \tau_{1}^*)$ are studied in $ZF$ and we prove some conditions hold in $ZF$.
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30

Osipov, Alexander V. "Selection principles and bitopological hyperspaces." Applied General Topology 24, no. 1 (2023): 1–8. http://dx.doi.org/10.4995/agt.2023.12424.

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In this paper we continue to research relationships between closure-type properties of hyperspaces over a space X and covering properties of X. For a Hausdorff space X we denote by 2X the family of all closed subsets of X. We investigate selection properties of the bitopological space (2X, Δ1+ , Δ2+) where Δi+ is the upper Δi-topology for each i=1,2.
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31

Mustafa, Hadi J., Rewayda Razaq Mohsin, and Enas Yehya Abdullah. "Pairwise Compact In Intuitionistic Double Topological Spaces." Journal of Kufa for Mathematics and Computer 1, no. 3 (2011): 70–76. http://dx.doi.org/10.31642/jokmc/2018/010309.

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The concept of intuitionistic topological space was introduced by Çoker .The aim of this paper is to discuss the relation between bitopological spaces and double- topological spaces and give a notion of pairwise compact for double topological spaces .
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32

Chentsov, Aleksandr Georgievich. "MAXIMAL LINKED SYSTEMS AND ULTRAFILTERS OF WIDELY UNDERSTOOD MEASURABLE SPACES." Tambov University Reports. Series: Natural and Technical Sciences, no. 124 (2018): 846–60. http://dx.doi.org/10.20310/1810-0198-2018-23-124-846-860.

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Two types of set families (ultrafilters or maximal filters and maximal linked systems) for widely understood measurable space are considered. The resulting sets of ultrafilters and maximal linked systems are equipped with the pair of comparable topologies (within the meaning of «Wallman» and «Stone»). As a result, two bitopological spaces are realized; one of them turns out a subspace of another. More precisely, ultrafilters are maximal linked systems and the totality of the latter forms a cumulative bitopological space. With employment of topological constructions some characteristic properti
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33

Salleh, Zabidin. "Pairwise Semiregular Properties on Generalized Pairwise Lindelöf Spaces." International Journal of Analysis and Applications 21 (March 3, 2023): 16. http://dx.doi.org/10.28924/2291-8639-21-2023-16.

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Let (X, τ1, τ2) be a bitopological space and (X, τs(1,2), τs(2,1)) its pairwise semiregularization. Then a bitopological property P is called pairwise semiregular provided that (X, τ1, τ2) has the property P if and only if (X, τs(1,2), τs(2,1)) has the same property. In this work we study pairwise semiregular property of (i, j)-nearly Lindelöf, pairwise nearly Lindelöf, (i, j)-almost Lindelöf, pairwise almost Lindelöf, (i, j)-weakly Lindelöf and pairwise weakly Lindelöf spaces. We prove that (i, j)-almost Lindelöf, pairwise almost Lindelöf, (i, j)-weakly Lindelöf and pairwise weakly Lindelöf a
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34

Thamizharasi, G., and P. Thangavelu. "Remarks on Closure and Interior Operators in Bitopological Spaces." Journal of Mathematical Sciences & Computer Applications 1, no. 1 (2017): 1–8. http://dx.doi.org/10.5147/jmsca.v1i1.85.

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Andrijevic and his collaborators studied the various aspects of closure and interior operators in general topological spaces and obtained several relations among them. Researchers in general topology studied such operators in bitopological settings. Andrijevic established that the result clA=Acl(int(clA)) holds for any subset A of a topological space where clA, clA and intA denote the -closure of A, closure of A and interior of A respectively. He also established the analog results for other operators in terms of the closure and interior operators in general topological spaces. In this pap
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35

Muturi, N. E., J. M. Khalagai, and G. P. Pokhariyal. "Separation axioms on function spaces defined on bitopological spaces." Journal of Advanced Studies in Topology 9, no. 2 (2018): 113–18. http://dx.doi.org/10.20454/jast.2018.1454.

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In this paper, we introduce separation axioms on the function space p− Cω(Y, Z) and study how they relateto separation axioms defined on the spaces (Z, δi) for i = 1, 2, (Z, δ1, δ2), 1 − Cς(Y, Z) and 2 − Cζ(Y, Z). Itis shown that the space p − Cω(Y, Z) is pT◦, pT1, pT2 and pregular, if the spaces (Z, δ1) and (Z, δ2) are bothT0, T1, T2 and regular respectively. The space p − Cω(Y, Z) is also shown to be pT0, pT1, pT2 and pregular,if the space (Z, δ1, δ2) is p − T0, p − T1, p − T2 and p-regular respectively. Finally, the space p − Cω(Y, Z) isshown to be pT0, pT1, pT2 and pregular, if and only if
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36

Bukhatwa, Ibtissam, та Sibel Demiralp. "On Generalized β-Open Sets in Ideal Bitopological Space". European Journal of Pure and Applied Mathematics 13, № 2 (2020): 269–79. http://dx.doi.org/10.29020/nybg.ejpam.v13i2.3649.

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In this article, we introduce and study the concepts of γij -semi-I-open sets and γij -βI-open sets by generalizing (i, j)-semi-I-open sets and (ij)-βI-open sets, respectively, in ideal bitopological spaces with an operation γ : τ → P(X). Further, we describe and study (γ, δ)ij -semi-I-continuous and (γ, δ)ij -βI-continuous functions in ideal bitopological spaces and their related notions. In addition, various examples and counterexamples are given for answers to some questions raised in this study.
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37

Abdrabo, Bara ,., and Hasan Hdeib. "Short Summary on Pairwise P-closed Bitopological Spaces." WSEAS TRANSACTIONS ON MATHEMATICS 21 (July 14, 2022): 533–39. http://dx.doi.org/10.37394/23206.2022.21.59.

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In this paper, we introduce the concept of pairwise P-closed spaces and obtain some of their properties. Furthermore, we generalize some results concerning P-closed spaces to pairwise P-closed. Eventually, we conclude that every p-paracompact, p.w.T2 bitopological space is p-normal.
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38

Ganster, M., and I. L. Reilly. "On pairwise paracompactness." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 53, no. 2 (1992): 281–85. http://dx.doi.org/10.1017/s1446788700035850.

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AbstractThis paper answers a recent question concerning the relationship between two notions of paracompactness for bitopological spaces. Romaguera and Marin defined pairwise paracompactness in terms of pair open covers, motivated by a characterization of paracompactness due to Junnila. On the other hand, Raghavan and Reilly defined a bitopological space (X, τ, σ) to be δ-pairwise paracompact if and only if every τ open (σ open) cover of X admits a τ V σ open refinement which is τ V σ locally finite. It is shown that pairwise paracompactness implies δ-pairwise paracompactness, and that the con
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39

Bukhatwa, Ibtissam, and Sibel Demiralp. "On Strong $(i,j)$-Semi$^{*}$-$\Gamma $-Open Sets in Ideal Bitopological Space." Journal of New Theory, no. 46 (March 28, 2024): 89–98. http://dx.doi.org/10.53570/jnt.1442116.

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In this study, we introduce the concepts of $(i,j)$-semi$^{*}$-$\Gamma $-open sets within the context of ideal bitopological spaces. This concept is demonstrated to be weaker than the established the notion of $(i,j)$-semi-$\Gamma $-open sets. Subsequently, we define strong $(i,j)$-semi$^{*}$-$\Gamma $-open sets in ideal bitopological spaces, elucidating some of their essential characteristics. Furthermore, leveraging this newly introduced concept, we establish the notions of strong $(i,j)$-semi$^{*}$-$\Gamma $-interior and strong $(i,j)$-semi$^{*}$-$\Gamma $-closure.
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40

Alkasasbeh, Bakr. "PROPERLY HEREDITARY PROPERTIES FOR SPECIAL BITOPOLOGICAL." Advances in Mathematics: Scientific Journal 11, no. 3 (2022): 125–29. http://dx.doi.org/10.37418/amsj.11.3.1.

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41

Aarts, J. M., and M. Mršević. "Pairwise complete regularity as a separation axiom." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 48, no. 2 (1990): 235–45. http://dx.doi.org/10.1017/s1446788700035667.

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AbstractFocussing on complete regularity, we discuss the separation properties of bitopological spaces. The unifying concept is that of separation by a pair of bases (B1, B2) for the closed sets of a bitopological space (S, J1, J2). For various separation properties a characterization is presented in terms of separation by a pair of closed bases. This is extended to results concerning pairs of subbases. Here the notion of screening by pairs of subbases plays a central role and the characterization of complete regularity in a natural way fits in between those of regularity and normality. In the
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42

Sarma, Diganta Jyoti, and Santanu Acharjee. "Some results on almost b-continuous functions in a bitopological space." Boletim da Sociedade Paranaense de Matemática 37, no. 2 (2017): 167–77. http://dx.doi.org/10.5269/bspm.v37i2.33618.

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43

P., Padma. "( τi , τj ) * - Q* g closed sets in Bitopological spaces". Journal of Progressive Research in Mathematics 2, № 1 (2015): 69–79. https://doi.org/10.5281/zenodo.3980807.

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The aim of this paper is to introduced the new type of closed sets called ( &tau;<sub>i</sub> , &tau;<sub>j</sub> )* - Q* g closed set . We introduce and study a new class of spaces namely (&tau;<sub>i</sub> , &tau;<sub>j</sub> )* - Q*g T1/2 space and ( &tau;<sub>i</sub> , &tau;<sub>j</sub> )* - Q* g T3/4 space . Also we find some basic properties and applications of ( &tau;<sub>i</sub> , &tau;<sub>j</sub> )* - Q* g closed sets .
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44

Sen, S. K., та M. N. Mukherjee. "On extension of pairwiseθ-continuous maps". International Journal of Mathematics and Mathematical Sciences 19, № 1 (1996): 53–56. http://dx.doi.org/10.1155/s0161171296000099.

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The aim of the paper is to find suitable conditions so as to ultimately establish the existence and uniqueness of the extension of a pairwiseθ-continuous map onto an arbitrary extension-space of a bitopological space.
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45

Saw, Ajay Kumar, and Binod Chandra Tripathy. "$H(i)$ Connected ditopological texture space." Boletim da Sociedade Paranaense de Matemática 37, no. 1 (2017): 87–97. http://dx.doi.org/10.5269/bspm.v37i1.34440.

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In this paper, we introduce the fundamental aspect of H(i) connected ditopological texture space, before proving we develop some basic key of bicontinuity and connectedness in term of ditopological texture space which will helpful in H(i) connected ditopological texture space. We establish some correspondence related to known structure such as bitopological space, fuzzy lattice and topological space.
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46

Chentsov, Aleksandr G. "Maximal linked systems and ultrafilters: main representations and topological properties". Russian Universities Reports. Mathematics, № 129 (2020): 68–84. http://dx.doi.org/10.20310/2686-9667-2020-25-129-68-84.

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Questions connected with representation of the ultrafilter (UF) set for widely understood measurable space are investigated; this set is considered as a subspace of bitopological space of maximal linked systems (MLS) under equipment with topologies of Wallman and Stone types (measurable structure is defined as a π -system with “zero” and “unit”). Analogous representations connected with generalized variant of cohesion is considered also; in this variant, for corresponding set family, it is postulated the nonemptyness of intersection for finite subfamilies with power not exceeding given. Condition
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47

Dr., C. Rajan. "ON (1, 2)*- - CLOSED SETS IN BITOPOLOGICAL SPACE." International Journal of Current Research and Modern Education, Special Issue (August 24, 2017): 148–55. https://doi.org/10.5281/zenodo.848255.

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In this paper, we offer a new class of sets called (1, 2)*--closed sets in bitopological spaces and we study some of its basic properties. It turns out that this class lies between the class of t<sub>1,2</sub>-closed sets and the class of (1, 2)*-g-closed sets.
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48

Dvalishvili, B. "Connectedness of a Fine Topology and Localization in Bitopological Spaces." gmj 11, no. 4 (2004): 713–32. http://dx.doi.org/10.1515/gmj.2004.713.

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Abstract The paper, consisting of four sections, of which Section 0 is auxiliary, is devoted to some principal questions of the theory of bitoplogical spaces. In Section 1, the 𝑝 -extremally disconnected, (𝑖, 𝑗)-strongly extremally disconnected and (𝑖, 𝑗)-nodec spaces are studied by means of the localization at a point. In Section 2, the (𝑖, 𝑗)-pseudoscattered, (𝑖, 𝑗)-ndscattered, 𝑝 -ultradisconnected and (𝑖, 𝑗)-Moscow spaces are introduced, their interrelations and their relations with the 𝑝 -extremally disconnected spaces are investigated, in particular, when one of the topologies is finer t
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49

Almuhur, Eman, Manal Al-Labadi, Maysoon Qousini та Raeesa Bashir. "Strongly 𝑫𝜶𝒑 −closed graphs in bitopological spaces". International Journal of ADVANCED AND APPLIED SCIENCES 11, № 9 (2024): 121–25. http://dx.doi.org/10.21833/ijaas.2024.09.013.

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In this paper, we introduce the concepts of D_α^p-open, D_α^p-closed subsets, pairwise-α-closed, pairwise-g-closed subsets, pairwise-strongly α-closed graph G(f) and strongly D_α^p-closed graph of bitopological spaces. We showed that each closed graph is D_α^p-closed. In addition, the concepts of D_α^p-continuous, open, and closed functions are defined, and the relations between τ_p-α, τ_p-g, and D_α^p-continuous functions are clarified. The fact that strongly D_α^p-closed graph is D_α^p-closed is illustrated. We studied when the graph G(f) is p-strongly closed and p-D_α-closed subsets of the
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50

Therese, Kulandhai, and Dilshad B. "Strongly (1,2)( ĝ )* Closed Sets In Bitopological Space." International Journal of Mathematics Trends and Technology 65, no. 6 (2019): 32–40. http://dx.doi.org/10.14445/22315373/ijmtt-v65i6p506.

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