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Journal articles on the topic 'Pi-closed and delta-closed sets'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

Hemlata, Sahay Hemlata Sahay. "MORE ABOUT πg eta-CLOSED SETS". International Journal of Current Science 12, № 2 (2022): 981–87. https://doi.org/10.5281/zenodo.14885341.

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In this paper, we study  πg eta-closed sets in topological spaces and investigate the relationship with other existing generalized closed sets. Moreover, we also study the concepts of  πg eta-continuous and almost  πg eta-continuous functions in topological spaces. We obtain some properties of πg eta-closed sets and almost  πg eta-continuous functions. A subset A of a space (X, ) is said to be gη-closed if η-cl(A)  U whenever A  U and U is -open in X. A function f : X → Y is called  πg eta- continuous if f &m

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2

Khedr, F. H., and O. R. Sayed. "DELTA GENERALIZED CLOSED AND GENERALIZED DELTA CLOSED SETS IN BITOPOLOGICAL SPACES." Universal Journal of Mathematics and Mathematical Sciences 14, no. 1 (2021): 13–28. http://dx.doi.org/10.17654/um014010013.

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3

Hamant, Kumar Hamant. "pi g eta-CLOSED SETS AND SOME RELATED TOPICS." Journal of Emerging Technologies and Innovative Research (JETIR) 8, no. 6 (2021): 367–74. https://doi.org/10.5281/zenodo.14885756.

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In this paper, we introduce a new class of sets called pi g eta-closed sets in topological spaces and investigate the relationship with other existing generalized closed sets. Moreover, we also introduce and studied the concepts of pi g eta-continuous and pi g eta-irresolute functions via pi g eta-closed sets which are defined by me. We obtain some properties about pi g eta-closed sets, pi g eta-continuous and pi g eta-irresolute functions, and pi g eta-compactness.

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4

Reepa, Biswas, Asokan R. та Premkumar R. "Nano (1,2)*-w πg Closed Sets and its Generalizations". International Journal of Mathematics and Computer Research 12, № 12 (2024): 4652–59. https://doi.org/10.5281/zenodo.14288791.

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In this paper, we introduce the notions of nano (1,2)*-<em>π-</em>closed sets and nano (1,2)*-<em>π</em>g-closed sets, nano (1,2)*-w<em>π</em>g -closed sets and nano (1,2)*-r<em>w</em>g-closed sets use it to obtain a characterization and preservation theorems of quasi-normal spaces.

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5

Keskin, Kaymakci A. "TWO SPECIAL GRAPHS FOR δ-B-OPEN SETS". Sciences of Europe, № 156 (6 січня 2025): 29–31. https://doi.org/10.5281/zenodo.14603419.

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6

Boonpok, Chawalit, and Napassanan Srisarakham. "Properties of Generalized $\delta p(\Lambda,s)$-closed Sets." European Journal of Pure and Applied Mathematics 16, no. 4 (2023): 2581–96. http://dx.doi.org/10.29020/nybg.ejpam.v16i4.4736.

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This paper deals with the concept of generalized $\delta p(\Lambda,s)$-closed sets. Especially, some properties of generalized $\delta p(\Lambda,s)$-closed sets are discussed. Moreover, we apply the notion of generalized $\delta p(\Lambda,s)$-closed sets to present and study new classes of spaces called $\delta p(\Lambda,s)$-$T_\frac{1}{2}$-spaces and $\delta p(\Lambda,s)$-normal spaces. Several properties and characterizations concerning $\delta p(\Lambda,s)$-$T_\frac{1}{2}$-spaces and $\delta p(\Lambda,s)$-normal spaces are established.

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7

Ankit, Gupta. "On \(\pi gs-\lambda\) Closed Sets in Generalized Topological Spaces." Journal of Advanced Studies in Topology 13, no. 1-2 (2023): 7–13. https://doi.org/10.5281/zenodo.7905124.

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In this paper, a new class of generalized closed sets called \(\pi gs-\lambda\) closed sets are introduced and some of its properties are studied. Along with this, the notion of \(\pi gs-\lambda\)-continuity and \(\pi gs-\lambda\)-\(T(1/2)\) spaces are introduced.

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8

Hamant, Kumar Hamant. "Quasi ξ- Normal Spaces and Gξ-Closed Sets". Online International Interdisciplinary Research Journal, {Bi-Monthly} 8, № 4 (2018): 134–42. https://doi.org/10.5281/zenodo.14898239.

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In this paper, we introduce the concept of gξ-closed sets as a weak form of    gclosed sets. By utilizing gξ-closed sets, we define gξ-closed, almost gξ-closed,      gξ-continuous and almost gξ-continuous functions. We also introduce the notion of quasi ξ-normal spaces and obtain a characterization and some preservation theorems for quasi       ξ-normal spaces. Further  we  show  that  this  property  is  a  topological  property  and  it  is  a hereditary  prop

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9

Hamant, Kumar Hamant. "piggjai*-CLOSED SETS AND QUASI gjai*-NORMAL SPACES." Journal of Emerging Technologies and Innovative Research (JETIR) 6, no. 5 (2019): 358–68. https://doi.org/10.5281/zenodo.14901317.

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 In this paper, we introduce a new class of sets called piggjai*-closed sets in topological spaces. Also we study and investigate the relationship with other existing closed sets. Moreover, we introduce some functions such as gjai*-closed, paiggjai*-closed, almost gjai*-closed, almost piggjai*-closed, piggjai*-continuous and almost piggjai*-continuous. We also study a new class of normal space called, quasi gjai*-normal space. The relationships among normal, pi-normal, quasi normal, softly normal, mildly normal, alpha-normal, pi alpha-normal, quasi alpha-normal, softly alpha-normal, mildl

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10

Hamant, Kumar Hamant. "On Q*g-closed sets." EPRA International Journal of Research and Development (IJRD) 9, no. 7 (2025): 189–90. https://doi.org/10.5281/zenodo.14872515.

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The author introduce the notion of Q*g-closed sets in the paper entitled Q*g-closed sets in topological space by P. Padma and S. Uday Kumar. However, there is a false theorem, namely Theorem 3.4. The correct statement of Theorem 3.4 is mentioned in this paper with correct proof and gave a counter-example in support of this theorem.

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11

Hamant, Kumar Hamant. "Quasi beeta-normal spaces and pi g beeta-closed functions." Acta Ciencia Indica XXXVIII M, no. 1 (2025): 149–54. https://doi.org/10.5281/zenodo.14866719.

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In this paper, by using pi g beeta-closed sets, we introduce some functions such as pi g beeta-closed, almost pigbeeta-closed, pigbeeta-continuous and almost pigbeeta-continuous functions. Further we obtain a characterization and preservation theorems for quasi beeta-normal spaces.

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12

Rajamani. "I_{\pi g}-Closed Sets and I_{\pi g}-Continuity." Journal of Advanced Research in Pure Mathematics 2, no. 4 (2010): 63–72. http://dx.doi.org/10.5373/jarpm.413.042010.

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13

Hamant, Kumar Hamant. "MORE ABOUT pigeta-CLOSED SETS." International Journal of Current Science (IJCSPUB) 12, no. 2 (2022): 981–87. https://doi.org/10.5281/zenodo.14880940.

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In this paper, we study pgeta-closed sets in topological spaces and investigate the relationship with other existing generalized closed sets. Moreover, we also study the concepts of pigeta-continuous and almost pigeta-continuous functions in topological spaces. We obtain some properties of pigeta-closed sets and almost pigeta-continuous functions. A subset A of a space (X, T) is said to be pigη-closed if η-cl(A)  U whenever A  U and U is pi-open in X. A function f : X → Y is called pigeta-continuous if f −1(F) is pigeta-closed in X for every closed set F of Y. A

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14

Selvaraj, Ganesan. "On micro forms of Delta-open sets, Delta-continuous maps and generalized micro Delta-continuous in micro topological spaces." Asia Mathematika 8, no. 2 (2024): 23——30. https://doi.org/10.5281/zenodo.13948738.

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This article introduces and studied m Delta-open sets in micro topological spaces. We offer a new class of sets called gm Delta-closed sets in micro topological spaces and we study some of its basic properties. The idea of introducing new classes of open sets are called micro semi Delta-open, micro alpha-Delta-open,  micro pre Delta-open,  micro b-Delta-open micro beta-Delta-open, micro regular Delta-open sets, micro semi Delta-continuous, micro alpha-Delta-continuous,  micro pre Delta-continuous, micro b-Delta-continuous micro beta-Delta-continuous and micro regular Delta-conti

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15

ÖZKOÇ, Murad, and Burcu Sünbül AYHAN. "On \(\pi ge\)-closed sets and related topics." Journal of Advanced Studies in Topology 7, no. 2 (2016): 93. http://dx.doi.org/10.20454/jast.2016.1021.

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16

V., Gopalakrishnan*1 M. Murugalingam2 &. R. Mariappan3. "ON πµ∗g-CLOSED SETS IN IDEAL GENERALIZED TOPOLOGICAL SPACES". GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, № 11 (2018): 348–52. https://doi.org/10.5281/zenodo.1624669.

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We  introduce  the  notions  of  πµ&lowast; g-closed  sets  by  using  the  notion of  µ-pre-I-open sets.  Further, we study the concept of πµ&lowast; g-closed sets and their relationships in an ideal generalized topological spaces by using these new notions.   2000 Mathematics Subject Classification: 54 A 05.  

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17

Benchalli, S. S., and J. B. Toranagatti. "Delta generalized pre-closed sets in topological spaces." International Journal of Contemporary Mathematical Sciences 11 (2016): 281–92. http://dx.doi.org/10.12988/ijcms.2016.6314.

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18

M., Vinoth, Asokan R., Ramesh V., and Premkumar R. "Binary pi generalized pre closed sets in binary topological spaces." Asia Mathematika 8, no. 2 (2024): 16——22. https://doi.org/10.5281/zenodo.13948719.

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19

Boonpok, Chawalit, and Montri Thongmoon. "$\delta p(\Lambda,p)$-open Sets in Topological Spaces." European Journal of Pure and Applied Mathematics 16, no. 3 (2023): 1533–42. http://dx.doi.org/10.29020/nybg.ejpam.v16i3.4733.

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This paper deals with the notion of $\delta p(\Lambda,p)$-open sets. Some properties of $\delta p(\Lambda,p)$-open sets and $\delta p(\Lambda,p)$-closed sets are investigated. Moreover, several characterizations of $\delta p(\Lambda,p)$-$\mathscr{D}_1$ spaces and $\delta p(\Lambda,p)$-$R_0$ spaces are established.

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20

N., Chandramathi, and Sujatha B. "$\delta \hat{g} $ Closed sets in grill topological spaces." Malaya Journal of Matematik 07, no. 04 (2019): 823–25. http://dx.doi.org/10.26637/mjm0704/0031.

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21

Meena, K., and K. Sivakamasundari. "Separation axioms by \Delta*-closed sets in topological spaces." International Journal of Mathematical Analysis 9 (2015): 927–34. http://dx.doi.org/10.12988/ijma.2015.5386.

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22

Vaishnavy, V., K. Sivakamasundari, and S. Jafari. "ON (\Lambda, \delta g)-CLOSED SETS IN TOPOLOGICAL SPACES." Far East Journal of Mathematical Sciences (FJMS) 101, no. 11 (2017): 2499–517. http://dx.doi.org/10.17654/ms101112499.

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23

Asia, Mathematika, and Ganesan Selvaraj. "Nano Delta Generalized-Locally Closed Sets in Nano Topological Spaces." Asia Mathematika 7, no. 3 (2024): 55——61. https://doi.org/10.5281/zenodo.10609824.

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The purpose of this paper is to introduce a new class of sets called generalized nano locally closed set in nanotopological spaces, also introduce generalized nanolocally continuous map, generalized nanolocally closed irresolute map and studied some of its properties. 

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24

Hamant, Kumar Hamant Kumar. "QUASI gamma-NORMAL SPACES IN TOPOLOGICAL SPACES." International Journal of Advance Research in Science and Engineering 5, no. 8 (2016): 451–58. https://doi.org/10.5281/zenodo.14901590.

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In  this  paper,  we  introduce  the  concept  of  piggamma-closed  sets  as  weak  form  of  pig-closed  sets. We  also  introduce the notion  of  quasi  gamma-normal  spaces  and  by using  g-closed  sets,  we  obtain  a  characterization  and  preservation  theorems  for  quasi gamma-normal  spaces. Further  we  show  that  this  property  is  a  topological  property &nbs

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25

Janaki, C., and D. Sreeja. "On Soft $\PI$GB-Closed Sets in Soft Topological Spaces." International Journal of Mathematics and Soft Computing 5, no. 1 (2015): 01. http://dx.doi.org/10.26708/ijmsc.2015.1.5.01.

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26

Mohana, K., and I. Arockiarani. "A Note on \((1,2)^{*}\)-Strongly-\(\pi g \alpha\)-Closed Sets." Journal of Advanced Studies in Topology 2, no. 2 (2011): 31. http://dx.doi.org/10.20454/jast.2011.224.

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27

Singh, Kushal, and Asha Gupta. "Semi-delta-open sets in topological space." Boletim da Sociedade Paranaense de Matemática 42 (April 19, 2024): 1–9. http://dx.doi.org/10.5269/bspm.62837.

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This purpose of this paper is to introduce a new class of open sets namely semi-delta-open sets . Further, some basic topological concepts such as neighbourhood axioms, border point, exterior point, frontier point of a set are defined and their properties have been investigated. In addition, in terms of these open sets, semi-delta-closed functions and semi-delta-continuous functions are also defined and their properties have been discussed

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28

MUKHERJEE, M. N., and S. RAYCHAUDHURI. "A NEW TYPE OF CLUSTER SETS AND ITS APPLICATIONS." Tamkang Journal of Mathematics 26, no. 4 (1995): 327–36. http://dx.doi.org/10.5556/j.tkjm.26.1995.4413.

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   In this paper we introduce the concept of a new type of cluster sets, termed $\delta$-cluster sets, of functions and multifunctions between topological spaces. Expressions of such sets are found and multifunctions with $\delta$-closed graphs are characterized. Also the behaviour of $\delta$-cluster sets toward a-continuity of a func- tion is observed. Finally as applications, we find new characterizations of almost regularity, near compactness and near Lindelofness of a topological space in terms of $\delta$-cluster sets of suitable multifunctions.   

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29

Latif, Raja Mohammad. "Delta – Open Sets And Delta – Continuous Functions." International Journal of Pure Mathematics 8 (February 9, 2021): 1–22. http://dx.doi.org/10.46300/91019.2021.8.1.

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In 1968 Velicko [30] introduced the concepts of δ-closure and δ-interior operations. We introduce and study properties of δ-derived, δ-border, δ-frontier and δ-exterior of a set using the concept of δ-open sets. We also introduce some new classes of topological spaces in terms of the concept of δ-D- sets and investigate some of their fundamental properties. Moreover, we investigate and study some further properties of the well-known notions of δ-closure and δ-interior of a set in a topological space. We also introduce δ-R0 space and study its characteristics. We also introduce δ-R0 space and s

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30

Capasso, Vincenzo, and Elena Villa. "ON MEAN DENSITIES OF INHOMOGENEOUS GEOMETRIC PROCESSES ARISING IN MATERIAL SCIENCE AND MEDICINE." Image Analysis & Stereology 26, no. 1 (2011): 23. http://dx.doi.org/10.5566/ias.v26.p23-36.

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The scope of this paper is to offer an overview of the main results obtained by the authors in recent literature in connection with the introduction of a Delta formalism, á la Dirac-Schwartz, for random generalized functions (distributions) associated with random closed sets, having an integer Hausdorff dimension n lower than the full dimension d of the environment space Rd. A concept of absolute continuity of random closed sets arises in a natural way in terms of the absolute continuity of suitable mean content measures, with respect to the usual Lebesgue measure on Rd. Correspondingly mean g

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31

Hamant, Kumar Hamant. "pigbeeta-Normal Spaces in Topological Spaces." International Journal of Science and Research (IJSR) 4, no. 2 (2025): 1531–34. https://doi.org/10.5281/zenodo.14866928.

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The aim of this paper is to introduce a new class of normal spaces called pigbeeta-normal spaces, by using pigbeeta-open  sets. We prove that pigbeeta-normality is a topological property and it is a hereditary property with respect to  pi-open, pigbeeta-closed subspaces. Further we obtain a characterization and preservation theorems for g-normal spaces. 

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32

Suleyman Guler. "On $\textit{I}_{\pi gs^{\star}}$-Closed Sets in Ideal Topological Spaces." Journal of Advanced Research in Pure Mathematics 3, no. 4 (2011): 120–27. http://dx.doi.org/10.5373/jarpm.764.020311.

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33

Sathishmohan, P., V. Rajendran, and P. Jeevitha. "On nano $pi g^ast$s-closed sets in nano topological spaces." Malaya Journal of Matematik 06, no. 03 (2018): 536–41. http://dx.doi.org/10.26637/mjm0603/0012.

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34

Hamant, Kumar Hamant. "pigb-NORMAL SPACES IN TOPOLOGICAL SPACES." Journal of Emerging Technologies and Innovative Research (JETIR) 6, no. 4 (2019): 15–25. https://doi.org/10.5281/zenodo.14891412.

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The aim of this paper is to introduce a new class of normal spaces, called gb-normal spaces by using pigb-closed and b-open sets. The relationships among pigp-normal, pigβ-normal, pigb-normal, p-normal, β-normal, gamma-normal, pi-normal, pip-normal, pibeeta normal, piβ-normal, almost normal, almost p-normal, almost gamma-normal, almost β-normal, quasi normal, quasi p-normal, quasi gamma-normal, quasi β-normal, mildly normal, mildly p-normal, mildly gamma-normal and mildly β-normal spaces are investigated. We also prove that pigb-normality is a topological pr

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35

Al-Omeri, Wadei Faris. "Double Fuzzy $\delta$-Continuous Functions in Double Fuzzy Topological Spaces." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 4624. https://doi.org/10.29020/nybg.ejpam.v18i2.4624.

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In this paper, we introduce $(\mathfrak{r}, \mathfrak{s})$-$\delta$-fuzzy closed sets in double fuzzy topological spaces and investigate some of their properties. Moreover, we introduce the concept of double fuzzy $\delta$-continuous functions. Several interesting properties and characterizations are introduced and discussed. Furthermore, the relationships among the new concepts are introduced and established with some interesting counterexamples.

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36

Selvaraj, Ganesan, and Smarandache Florentin. "Some new classes of neutrosophic minimal open sets." Asia Mathematika 5, no. 1 (2021): 103–12. https://doi.org/10.5281/zenodo.4724804.

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This article focuses on \(N_m- \beta\)-open, \(\beta\)-interior and \(\beta\)-closure operators using neutrosophic minimal structures. We investigate the properties of such concepts and we introduced the concepts of \(N_m- \beta\)-continuous,  \(N_m- \beta\)-closed graph, \(N_m- \beta\)-compact and almost \(N_m- \beta\)-compact. Finally, we introduced the concepts of \(N_m-\)regular-open sets and \(N_m-\pi\)-open sets and investigate some properties.

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37

Hamant, Kumar Hamant. "Softly normal topological spaces." Acta Ciencia Indica VLI M, no. 2 (2025): 81–84. https://doi.org/10.5281/zenodo.14866870.

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In the present paper, we introduce a weaker version of normality called  softly normality. We will prove that softly normality is a property, which is implied by quasi normality and almost normality. We prove that soft normality is a topological property and it is a hereditary property with respect to closed domain subspace.

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38

Valenti, Manlio. "A journey through computability, topology and analysis." Bulletin of Symbolic Logic 28, no. 2 (2022): 266–67. http://dx.doi.org/10.1017/bsl.2022.13.

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AbstractThis thesis is devoted to the exploration of the complexity of some mathematical problems using the framework of computable analysis and (effective) descriptive set theory. We will especially focus on Weihrauch reducibility as a means to compare the uniform computational strength of problems. After a short introduction of the relevant background notions, we investigate the uniform computational content of problems arising from theorems that lie at the higher levels of the reverse mathematics hierarchy.We first analyze the strength of the open and clopen Ramsey theorems. Since there is

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39

Bounkhel, Messaoud. "Generalized $ (f, \lambda) $-projection operator on closed nonconvex sets and its applications in reflexive smooth Banach spaces." AIMS Mathematics 8, no. 12 (2023): 29555–68. http://dx.doi.org/10.3934/math.20231513.

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<abstract><p>In this paper, we expanded from the convex case to the nonconvex case in the setting of reflexive smooth Banach spaces, the concept of the $ f $-generalized projection $ \pi^{f}_S:X^*\to S $ initially introduced for convex sets and convex functions in <sup>[<xref ref-type="bibr" rid="b19">19</xref>,<xref ref-type="bibr" rid="b20">20</xref>]</sup>. Indeed, we defined the $ (f, \lambda) $-generalized projection operator $ \pi^{f, \lambda}_S:X^*\to S $ from $ X^* $ onto a nonempty closed set $ S $. We proved many properties of $ \pi^{f,

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40

Urrea-Quintero, Jorge-Humberto, Jan N. Fuhg, Michele Marino, and Amélie Fau. "PI/PID controller stabilizing sets of uncertain nonlinear systems: an efficient surrogate model-based approach." Nonlinear Dynamics 105, no. 1 (2021): 277–99. http://dx.doi.org/10.1007/s11071-021-06431-1.

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AbstractClosed forms of stabilizing sets are generally only available for linearized systems. An innovative numerical strategy to estimate stabilizing sets of PI or PID controllers tackling (uncertain) nonlinear systems is proposed. The stability of the closed-loop system is characterized by the sign of the largest Lyapunov exponent (LLE). In this framework, the bottleneck is the computational cost associated with the solution of the system, particularly including uncertainties. To overcome this issue, an adaptive surrogate algorithm, the Monte Carlo intersite Voronoi (MiVor) scheme, is adopte

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41

Dawood, Suliman, and Adem Kilicman. "On $\theta(\Delta)-$open sets in grill topological spaces." Journal of Mathematical Analysis and Modeling 5, no. 2 (2024): 44–52. https://doi.org/10.48185/jmam.v5i2.986.

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The objective of this paper is to present and examine these concepts within the context of grill topolog ical spaces, introducing novel categories of θ(∆)−closed sets and θ(∆)−continuous functions specific to grilltopological spaces.

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42

Muthuswamy, Myvizhi. "On <i>S*</i> <i>gα</i>-in Terms of <i>M</i>-Structure Spaces of Continuous and Irresolute Functions". HyperSoft Set Methods in Engineering 2 (26 червня 2024): 28–37. http://dx.doi.org/10.61356/j.hsse.2024.2311.

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The paper is an introduction to Minimal structure spaces and their properties. The extension of indiscrete topology is known as minimal structure. Indiscrete topology contains only an empty set and a universal set. The minimal structure contains an empty set, a universal set and it may also contain any subset of universal set but it should satisfy the first axiom of topology. We introduce the terms of Minimal delta star g alpha closed sets and also study a new class of functions namely Minimal delta star g alpha continuous and Minimal delta star g alpha irresolute function.

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43

Chentsov, Alexander G. "PRODUCTS OF ULTRAFILTERS AND MAXIMAL LINKED SYSTEMS ON WIDELY UNDERSTOOD MEASURABLE SPACES." Ural Mathematical Journal 7, no. 2 (2021): 3. http://dx.doi.org/10.15826/umj.2021.2.001.

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Constructions related to products of maximal linked systems (MLSs) and MLSs on the product of widely understood measurable spaces are considered (these measurable spaces are defined as sets equipped with \(\pi\)-systems of their subsets; a \(\pi\)-system is a family closed with respect to finite intersections). We compare families of MLSs on initial spaces and MLSs on the product. Separately, we consider the case of ultrafilters. Equipping set-products with topologies, we use the box-topology and the Tychonoff product of Stone-type topologies. The properties of compaction and homeomorphism hol

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44

Mohammed, Ramadhan A., O. R. Sayed, and A. Eliow. "Some Properties of Soft Delta-Topology." Academic Journal of Nawroz University 8, no. 4 (2019): 352. http://dx.doi.org/10.25007/ajnu.v8n4a481.

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In this paper, we apply the concept of soft sets to δ-open set and δ-closed set. The associated soft δ-topology in terms of soft δ-open sets were introduced and some properties of them were investigated. Moreover, the definitions, characterizations and basic results concerning soft δ-interior, soft δ-closure, soft δ-boundary and soft δ-exterior were given. Finally, the concept of soft pu−δ- continuity was defined and some properties of it were introduced.

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45

Hamant, Kumar Hamant. "SILKY NORMAL SPACES IN TOPOLOGICAL SPACES." Journal of Emerging Technologies and Innovative Research (JETIR) 6, no. 6 (2019): 233–40. https://doi.org/10.5281/zenodo.14901392.

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The aim of this paper is to introduce and study a new class of normal spaces, called silky-normal spaces. Interrelation among some existing variants of normality is discussed and characterizations of these variants are obtained. We also proved that silk normality is a topological property and it is a hereditary property with respect to closed domain subspace. The decomposition of normality in terms of silky normality and some factorizations of normality in presence of some lower separation axioms are given

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46

Pochynyuk, Oleh, Vladislav Bugaj, Alain Vandewalle, and James D. Stockand. "Purinergic control of apical plasma membrane PI(4,5)P2 levels sets ENaC activity in principal cells." American Journal of Physiology-Renal Physiology 294, no. 1 (2008): F38—F46. http://dx.doi.org/10.1152/ajprenal.00403.2007.

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Activity of the epithelial sodium channel (ENaC) is limiting for Na+ reabsorption at the distal nephron. Phosphoinositides, such as phosphatidylinositol 4,5-biphosphate [PI(4,5)P2] modulate the activity of this channel. Activation of purinergic receptors triggers multiple events, including activation of PKC and PLC, with the latter depleting plasma membrane PI(4,5)P2. Here, we investigate regulation of ENaC in renal principal cells by purinergic receptors via PLC and PI(4,5)P2. Purinergic signaling rapidly decreases ENaC open probability and apical membrane PI(4,5)P2 levels with similar time c

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Matušů, Radek, and Roman Prokop. "Robust Stability of Fractional Order Time-Delay Control Systems: A Graphical Approach." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/847210.

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The paper deals with a graphical approach to investigation of robust stability for a feedback control loop with an uncertain fractional order time-delay plant and integer order or fractional order controller. Robust stability analysis is based on plotting the value sets for a suitable range of frequencies and subsequent verification of the zero exclusion condition fulfillment. The computational examples present the typical shapes of the value sets of a family of closed-loop characteristic quasipolynomials for a fractional order plant with uncertain gain, time constant, or time-delay term, resp

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HUMPHRIES, STEPHEN P. "SOME LINEAR REPRESENTATIONS OF BRAID GROUPS." Journal of Knot Theory and Its Ramifications 09, no. 03 (2000): 341–66. http://dx.doi.org/10.1142/s0218216500000165.

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In this paper we exhibit a way of obtaining linear representations of the braid groups Bn over ℤ[t] by studying their action on the set of isotopy classes of sets of simple closed curves on a punctured disc. The cases n=3, 4, 5 are shown to be very different from the cases n>5. We show a connection between representations of B3 and Pascal's triangle. We also show that there is a sequence of polynomials κi(t), i≥0, related to polynomials Pi(t) defined by V. F. R. Jones all of whose roots give values of t for which these representations are not faithful.

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Al-Ghour, Samer, and Hanan Al-Saadi. "Soft weakly connected sets and soft weakly connected components." AIMS Mathematics 9, no. 1 (2023): 1562–75. http://dx.doi.org/10.3934/math.2024077.

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<abstract><p>Although the concept of connectedness may seem simple, it holds profound implications for topology and its applications. The concept of connectedness serves as a fundamental component in the Intermediate Value Theorem. Connectedness is significant in various applications, including geographic information systems, population modeling and robotics motion planning. Furthermore, connectedness plays a crucial role in distinguishing between different topological spaces. In this paper, we define soft weakly connected sets as a new class of soft sets that strictly contains the

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Orponen, Tuomas. "Additive properties of fractal sets on the parabola." Annales Fennici Mathematici 48, no. 1 (2023): 113–39. http://dx.doi.org/10.54330/afm.125826.

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Let \(0 \leq s \leq 1\), and let \(\mathbb{P} := \{(t,t^{2}) \in \mathbb{R}^{2} \colon t \in [-1,1]\}\). If \(K \subset \mathbb{P}\) is a closed set with \(\operatorname{dim}_{\mathrm{H}} K = s\), it is not hard to see that \(\operatorname{dim}_{\mathrm{H}} (K + K) \geq 2s\). The main corollary of the paper states that if \(0 < s < 1\), then adding \(K\) once more makes the sum slightly larger: \( \operatorname{dim}_{\mathrm{H}} (K + K + K) \geq 2s + \epsilon,\)where \(\epsilon = \epsilon(s) > 0\). This information is deduced from an \(L^{6}\) bound for the Fourier transforms of Frost

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