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Journal articles on the topic 'A-closed sets'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Roy, Bishwambhar, та Ritu Sen. "On a class of sets betweenμ-closed sets andμg-closed sets". Journal of Taibah University for Science 11, № 2 (2017): 268–73. http://dx.doi.org/10.1016/j.jtusci.2015.08.008.

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2

Rajiv, Kumar Mishra. "Application of some notations in Topological Spaces." MATHEMATICS EDUCATION LV, no. 2, June 2021 (2021): 43–53. https://doi.org/10.5281/zenodo.7376235.

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               We have introduced some notations in topological spaces and with its help conditions for continuity, semi-continuity, semi-open sets, semi-closed sets, etc. have been deduced.

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3

Jackson, S., and J. Sivasankar. "A New Class of Generalized Closed Sets in Pentapartitioned Neutrosophic Topological Spaces." Indian Journal Of Science And Technology 17, SPI1 (2024): 14–20. http://dx.doi.org/10.17485/ijst/v17sp1.113.

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Objective: The motive of this research paper is to give a new notion called Pentapartitioned Neutrosophic Generalized Pre Open and Closed sets. Methods: To get the Pentapartitioned Neutrosophic Generalized Pre Open and Closed sets, PN topology is needed. Further, there is a need to find the Pre Open and Pre Closed sets and then we use our definition to get the required objective. Findings: The Pentapartitioned Neutrosophic Generalized Pre sets give a more finer collection of weak sets. Moreover, we can find the interior, exterior, and frontier of the resultant set. Novelty: Finding the general

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4

Cao, Jiling, Sina Greenwood, and Ivan L. Reilly. "Generalized closed sets: a unified approach." Applied General Topology 2, no. 2 (2001): 179. http://dx.doi.org/10.4995/agt.2001.2148.

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We investigate various classes of generalized closed sets of a topological space in a unified way by studying the notion of qr-closed sets. New characterizations of some existing classes of generalized closed sets and topological spaces are given. A new class of generalized closed sets are introduced.

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5

Vaishnavy, V. *. Sivakamasundari K. "A NEW GENERALIZATION OF 𝛿-CLOSED SETS USING TWO DIFFERENT OPERATORS". INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 5, № 9 (2016): 791–95. https://doi.org/10.5281/zenodo.155246.

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The scope of this paper is to give a new generalization to 𝛿-closed sets namely -closed sets which involves the use of two different operators. Some interesting theorems involving -closed sets are discussed.

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6

J., B. TORANAGATTI. "A NOTE ON REGULAR GENERALIZED B-CLOSED SETS IN TOPOLOGICAL SPACES." Asian Journal of Current Research 2, no. 1 (2017): 20–21. https://doi.org/10.5281/zenodo.1408486.

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In this article, we point out that the collection of rgb-closed sets due to K. Mariappa and S. Sekar [1] means nothing to a power set. Further, we also established that the concepts of rgb-closed sets and gspr-closed sets are same.

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7

Li, Zhongshan. "A determinantal description of GCD-closed sets andk-sets." Linear and Multilinear Algebra 31, no. 1-4 (1992): 245–50. http://dx.doi.org/10.1080/03081089208818137.

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8

Granados, Carlos. "A new decomposition of open and closed sets in topological spaces." Selecciones Matemáticas 8, no. 1 (2021): 66–74. http://dx.doi.org/10.17268/sel.mat.2021.01.06.

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9

Baker, C. W. "A note onθ-generalized closed sets". International Journal of Mathematics and Mathematical Sciences 25, № 8 (2001): 559–63. http://dx.doi.org/10.1155/s0161171201003945.

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The purpose of this note is to strengthen several results in the literature concerning the preservation ofθ-generalized closed sets. Also conditions are established under which images and inverse images of arbitrary sets areθ-generalized closed. In this process several new weak forms of continuous functions and closed functions are developed.

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10

Azzam, A. A. "A New Closed Set in Topological Spaces." Mathematical Problems in Engineering 2021 (May 31, 2021): 1–4. http://dx.doi.org/10.1155/2021/6617224.

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Our purpose of this work is to implement a class of s g ^ -closed sets, which is property placed among the classes of semiclosed sets and g s -closed sets. The relations with other concepts directly or indirectly joined with generalized closed sets are inspected. In addition, as an application, using the notion of s g ^ -closed sets, we give a brief expansion of a new space named T s g ^ -space.

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11

Y., Gh. Gouda, M. El-Sharkasy M. та M. El-Sayed S. "New types of generalizations of θ- closed sets". Journal of Progressive Research in Mathematics 8, № 2 (2016): 1249–57. https://doi.org/10.5281/zenodo.3976773.

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The aim of this paper is to introduce and study the class of <em>T</em>-closed sets as a generalization of θ-closed sets, which is properly placed between θ-closed sets and closed sets. A generalization of <em>T</em>- closed sets, namely, generalized T-closed sets is introduced and studied, which is properly placed between T-closed sets and g-closed sets.

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12

Khudair, Huda F., and Fatimah M. Mohammed. "Generalized of A-Closed Set and Ƈ- Closed Set in Fuzzy Neutrosophic Topological Spaces." International Journal of Neutrosophic Science 19, no. 2 (2022): 08–18. http://dx.doi.org/10.54216/ijns.190201.

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In this research paper, a new two classes of sets called fuzzy neutrosophic generalized A-closed sets and fuzzy neutrosophic generalized Ƈ-Closed sets in fuzzy neutrosophic topology are introduced and some of their properties have been investigated. We give some theorems, propositions and some necessary examples related to presented definitions. Then, we discuss the relations among the new defined sets.

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13

Raviraj R and Mohamed Ali A. "A study on J(**) - closed sets in topological spaces." Journal of Computational Mathematica 8, no. 1 (2024): 033–37. http://dx.doi.org/10.26524/cm184.

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The concept of J(**) - closed sets in initiated here. A few interesting peculiarities of J(**) - closed sets are discussed. Moreover relations of J(**) - closed sets with other existing G-closed sets are analysed. Some important characterizations are also obtained.

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14

Ganter, Bernhard, and Klaus Reuter. "Finding all closed sets: A general approach." Order 8, no. 3 (1991): 283–90. http://dx.doi.org/10.1007/bf00383449.

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15

Mohammed, Ramadhan A., Tahir H. Ismail та A. A. Allam. "A comment on generalized αβ-closed sets". Journal of the Egyptian Mathematical Society 25, № 1 (2017): 57–58. http://dx.doi.org/10.1016/j.joems.2016.06.004.

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16

Al-Saadi, H. S. "A bitopological (1,2)*-\lambda-generalized closed sets." International Journal of Mathematical Analysis 10 (2016): 51–60. http://dx.doi.org/10.12988/ijma.2016.511291.

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17

Pachón, Néstor Raúl. "Between closed and Ig-closed sets." European Journal of Pure and Applied Mathematics 11, no. 1 (2018): 299. http://dx.doi.org/10.29020/nybg.ejpam.v11i2.3131.

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The concept of closed sets is a central object in general topology. In order to extend many of important properties of closed sets to a larger families, Norman Levine initiated the study of generalized closed sets. In this paper we introduce, via ideals, new generalizations of closed subsets, which are strong forms of the Ig-closed sets, called ρIg-closed sets and closed-I sets. We present some properties and applications of these new sets and compare the ρIg-closed sets and the closed-I sets with the g-closed sets introduced by Levine. We show that Iclosed and closed-I are independent concept

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18

Riyadh Kareem, Noor, and . "Fuzzy tgp-closed sets and fuzzy t^* gp-closed sets." International Journal of Engineering & Technology 7, no. 4.36 (2018): 718. http://dx.doi.org/10.14419/ijet.v7i4.36.24229.

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In this paper, we aim to address the idea of fuzzy -set and fuzzy -set in fuzzy topological space to present new types of the fuzzy closed set named fuzzy -closed set and fuzzy -closed set. We will study several examples and explain the relations of them with other classes of fuzzy closed sets. Moreover, in a fuzzy locally indiscrete space we can see that these two sets are the same.

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19

Porter, Jack, and Mohan Tikoo. "Separating H-sets by Open Sets." Canadian Mathematical Bulletin 53, no. 2 (2010): 360–66. http://dx.doi.org/10.4153/cmb-2010-039-x.

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AbstractIn an H-closed, Urysohn space, disjoint H-sets can be separated by disjoint open sets. This is not true for an arbitrary H-closed space even if one of the H-sets is a point. In this paper, we provide a systematic study of those spaces in which disjoint H-sets can be separated by disjoint open sets.

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20

Al-Zoubi, Khalid Y. "On generalizedω-closed sets". International Journal of Mathematics and Mathematical Sciences 2005, № 13 (2005): 2011–21. http://dx.doi.org/10.1155/ijmms.2005.2011.

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The class ofω-closed subsets of a space(X,τ)was defined to introduceω-closed functions. The aim of this paper is to introduce and study the class ofgω-closed sets. This class of sets is finer thang-closed sets andω-closed sets. We study the fundamental properties of this class of sets. In the space(X,τω), the concepts closed set,g-closed set, andgω-closed set coincide. Further, we introduce and studygω-continuous andgω-irresolute functions.

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21

MATOUšKOVA, EVA. "TRANSLATING FINITE SETS INTO CONVEX SETS." Bulletin of the London Mathematical Society 33, no. 6 (2001): 711–14. http://dx.doi.org/10.1112/s0024609301008372.

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Let X be a reflexive Banach space, and let C ⊂ X be a closed, convex and bounded set with empty interior. Then, for every δ > 0, there is a nonempty finite set F ⊂ X with an arbitrarily small diameter, such that C contains at most δ · |F| points of any translation of F. As a corollary, a separable Banach space X is reflexive if and only if every closed convex subset of X with empty interior is Haar null.

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22

Altoumi, Nadiy A., and Fatma A. Toumi. "On P^* g- Closed Set in topological Spaces." International Science and Technology Journal 36, no. 1 (2025): 1–10. https://doi.org/10.62341/nafa3003.

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Closed sets play a fundamental role in topological spaces. Notably, a topology on a set can even be characterized by specifying the properties of its closed sets. In 1970, N. Levine introduced the concept of generalized closed sets, defined: A subset S of a topological space X is considered generalized closed if the closure of A is contained in U, cl(A)⊆U whenever A⊆U and U is open set. In this study, we define and explore novel classes of sets termed pre star generalized closed sets (P^* g-closed), pre star generalized open sets (P^* g-open) within the context of topological spaces. The relat

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23

Al-Omari, Ahmad, and Takashi Noiri. "A Generalization of mg-closed sets in Hereditary m-spaces." Acta et Commentationes Universitatis Tartuensis de Mathematica 27, no. 2 (2023): 147–56. http://dx.doi.org/10.12697/acutm.2023.27.12.

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In this paper, we introduce the notion of mgH-closed sets in a hereditary m-space (X, m, H) and obtain a further generalization of mg-closed sets. We investigate basic properties, characterizations and preservation properties of mgH-closed sets.

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24

ECCLES, TOM. "A Stability Result for the Union-Closed Size Problem." Combinatorics, Probability and Computing 25, no. 3 (2015): 399–418. http://dx.doi.org/10.1017/s0963548315000176.

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A family of sets is called union-closed if whenever A and B are sets of the family, so is A ∪ B. The long-standing union-closed conjecture states that if a family of subsets of [n] is union-closed, some element appears in at least half the sets of the family. A natural weakening is that the union-closed conjecture holds for large families, that is, families consisting of at least p02n sets for some constant p0. The first result in this direction appears in a recent paper of Balla, Bollobás and Eccles [1], who showed that union-closed families of at least $\tfrac{2}{3}$2n sets satisfy the conje

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25

ali, R. S. W., and Vijaykumari T.Chilakwad. "Pre Generalized Regular Weakly-Closed (pgrw-closed) Sets in a Bitopological Space." International Journal of Mathematics Trends and Technology 54, no. 5 (2018): 355–65. http://dx.doi.org/10.14445/22315373/ijmtt-v54p541.

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26

Şaşmaz, Pınar, та Murad Özkoç. "Generalized ωe∗-closed Sets". European Journal of Pure and Applied Mathematics 15, № 2 (2022): 354–74. http://dx.doi.org/10.29020/nybg.ejpam.v15i2.4340.

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The aim of this paper is to introduce and study a new type of generalized closed sets, called generalized ωe∗ -closed (briefly, gωe∗ -closed) sets, via ωe∗-closure operator. We examine the fundamental properties of the class of these sets. The notion of gωe∗-closed set is weaker than the notions of gωβ-closed set and ωe∗-closed set in the literature. Also, we define and discuss the notions of generalized ωe∗-continuous and generalized ωe∗-irresolute functions.

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27

Elumalai,, Dr N., and Kalpana R. "The Mersenne Meet Matrices with A – Sets on Exponential Divisor Closed Sets." International Journal of Research in Advent Technology 7, no. 5 (2019): 661–64. http://dx.doi.org/10.32622/ijrat.752019134.

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28

Norton, R. M., and D. G. Sarvate. "A note of the union-closed sets conjecture." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 55, no. 3 (1993): 411–13. http://dx.doi.org/10.1017/s1446788700034133.

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AbstractLet = {A1, …, An} be a union-closed set. This note establishes a property which must be possessed by any smallest counterexample to the Union-Closed Sets Conjecture. Specifically, a counterexample to the conjecture with minimal n has at least three distinct elements, each of which appears in exactly (n − 1)/2 of the .

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29

Al-Omari, Ahmad, та Mohd Salmi Md Noorani. "Regular Generalizedω-Closed Sets". International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–11. http://dx.doi.org/10.1155/2007/16292.

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In 1982 and 1970, Hdeib and Levine introduced the notions ofω-closed set and generalized closed set, respectively. The aim of this paper is to provide a relatively new notion of generalized closed set, namely, regular generalizedω-closed, regular generalizedω-continuous,a-ω-continuous, and regular generalizedω-irresolute maps and to study its fundamental properties.

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30

R., Subasree, Basari Kodi K., Sathikala L., and Subramanian K. "A Study on various Pentapartitioned Neutrosophic generalized closed sets." International Journal of Neutrosophic Science 20, no. 4 (2023): 235–40. http://dx.doi.org/10.54216/ijns.200419.

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The purpose of this paper is to introduce the concept of various Pentapartitioned neutrosophic generalized closed sets such as PNg-closed set, PNω-closed set, PNgb-closed set in Pentapartitioned Neutrosophic Topological spaces. We also study some of their properties with counter examples.

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31

Kowsalya, M., та D. Jayanthi. "µ-β-generalized α-closed sets in generalized topological spaces". International Journal of Trend in Scientific Research and Development 2, № 3 (2018): 2318–20. https://doi.org/10.31142/ijtsrd11665.

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In this paper, we have introduced a new class of sets in generalized topological spaces called µ Ã&Yuml; generalized a closed sets. Also we have investigated some of their basic properties. Kowsalya M | Jayanthi D "µ-Î²-generalized Î±-closed sets in generalized topological spaces" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-3 , April 2018, URL: https://www.ijtsrd.com/papers/ijtsrd11665.pdf

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32

Ekici, Erdal, and Nur Tunç. "On a superclass of *-operfectness." Filomat 31, no. 14 (2017): 4499–505. http://dx.doi.org/10.2298/fil1714499e.

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This paper presents P*-closed sets defined by using the sets in ideal. This concept is a new approach on the sets of ideal spaces. The class of P*-closed sets is a superclass of *-operfect sets and *-open pre*I -closed sets.

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33

Faro, Giovanni Lo. "A note on the union-closed sets conjecture." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 57, no. 2 (1994): 230–36. http://dx.doi.org/10.1017/s1446788700037526.

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AbstractIt has been conjectured that for any union-closed set there exists some element which is contained in at least half the sets in . It is shown that this conjecture is true if the number of sets in is less than 25. Several conditions on a counterexample are also obtained.

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34

Joseph, James E., and Bhamini M. P. Nayar. "A Hausdorff (Urysohn) [Regular] Space In Which Closed Sets are Hausdorff-Closed (Urysohn-Closed) [Rgular-Closed] Is Compact." Journal of Advanced Studies in Topology 5, no. 1 (2013): 6. http://dx.doi.org/10.20454/jast.2014.692.

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35

Kosman, Jolanta. "Separating sets by functions with a closed graph." Quaestiones Mathematicae 40, no. 5 (2017): 623–26. http://dx.doi.org/10.2989/16073606.2017.1305462.

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36

Alli, K., A. Subramanian, and S. Pious Missier. "G#P#-Closed Sets in a Topological Spaces." International Journal of Mathematics and Soft Computing 3, no. 3 (2013): 55. http://dx.doi.org/10.26708/ijmsc.2013.3.3.08.

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37

Ganster, Maximilian. "A NOTE ON EXTENSIONS GENERATED BY CLOSED SETS." Tamkang Journal of Mathematics 26, no. 2 (1995): 125–29. http://dx.doi.org/10.5556/j.tkjm.26.1995.4386.

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   In a recent paper Abd El-Monsef et al. consider a certain topology on $2^X$ where $2^X$ is the family of all nonempty closed subsets of a given topological space $X$. Vnfortunately, several results in their paper are incorrect and so the purpose of this note is to correct, improve and expand these results. In addition, the main quesion in their paper turns out to have a quite simple answer.   

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38

Indirani, K., P. Sathishmohan, and V. Rajendran. "On gr*-Closed Sets in a Topological Spaces." International Journal of Mathematics Trends and Technology 6, no. 2 (2014): 142–48. http://dx.doi.org/10.14445/22315373/ijmtt-v6p514.

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39

Noiri, Takashi. "A unified theory for modifications ofg-closed sets." Rendiconti del Circolo Matematico di Palermo 56, no. 2 (2007): 171–84. http://dx.doi.org/10.1007/bf03031437.

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40

A., Punitha Tharani. "A New Class of Nano Generalized Star Beta Closed Sets in Nano Topological Spaces." Journal of Advanced Research in Dynamical and Control Systems 12, SP4 (2020): 1088–94. http://dx.doi.org/10.5373/jardcs/v12sp4/20201582.

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41

admin, admin, and G. Chandra Ray. "A new class of NeutroOpen, NeutroClosed, AntiOpen and AntiClosed sets in NeutroTopological and AntiTopological spaces." International Journal of Neutrosophic Science 20, no. 2 (2023): 77–85. http://dx.doi.org/10.54216/ijns.200206.

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A lot of research has been done on the types of open and closed sets in general topological spaces and also in general bitopological spaces. Types of sets like pre-open sets and pre-closed sets, semi-open sets and semi-closed sets, Alpha-open sets, and Alpha-closed sets, regular open sets and regular closed sets, g-open sets and g-closed sets, and many more have been defined and studied. In the current study, an attempt has been made to define and give examples of a new category of open and closed sets, namely, NeutroOpen and NeutroClosed sets. Further, the concept of neutron-topology is used

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42

Kowsalya, M., та M. Sentamilselvi. "Contra µ-β-Generalized α-Continuous Mappings in Generalized Topological Spaces". International Journal of Trend in Scientific Research and Development 2, № 6 (2018): 607–11. https://doi.org/10.31142/ijtsrd18584.

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In this paper, we have introduced contra µ Ã&Yuml; generalized a continuous maps and also introduced almost contra µ Ã&Yuml; generalized a continuous maps in generalized topological spaces by using µ Ã&Yuml; generalized a closed sets briefly µ Ã&Yuml;GaCS . Also we have introduced some of their basic properties. Kowsalya M | Sentamilselvi M "Contra µ-Î²-Generalized Î±-Continuous Mappings in Generalized Topological Spaces" Published in International Journal of Trend in Scientific Research and Development

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43

Alrikabiu, Ahmed Hussein Wajan, та Ali Khalaf Hussain. "γpg**- Closed Set in Topological Spaces". Wasit Journal of Pure sciences 2, № 1 (2023): 173–83. http://dx.doi.org/10.31185/wjps.86.

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Abstract  In this paper we investigate the definitions of g-closed sets, gp-closed sets, pg-closed sets, gsp-closed sets, g -closed sets, g-closed sets. we introduced a new class of set called γpg**-closed sets which is settled properly in between the class of semi-closed and the class of g**-closed sets .

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44

Hamant, Kumar Hamant. "RGeta-Closed Sets in Topological Spaces." International Journal of Science and Research (IJSR) 10, no. 11 (2025): 1138–42. https://doi.org/10.5281/zenodo.14880792.

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In this paper, a new class of sets called regular generalized eta-closed (briefly rgη-closed) sets is introduced and its propertiesare studied. The relationships among closed, alpha-closed, s-closed, η-closed, rgη-closed and their generalized closed sets are investigated. Several examples are provided to illustrate the behavior of these new class of sets.

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45

J., Carolinal, та Anto M. "A STUDY ON Nˆg∗s− CLOSED SETS IN NANO TOPOLOGICAL SPACES". South East Asian Journal of Mathematics and Mathematical Sciences 19, № 02 (2023): 379–92. http://dx.doi.org/10.56827/seajmms.2023.1902.28.

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In this paper, we define and study about a new type of Nano generalizedclosed set called Nˆg∗s−closed sets in nano topological space. The relationshipof Nˆg∗s−closed sets with other known Nano generalized closed sets and the characteristicsof Nˆg∗s−interior, Nˆg∗s−exterior, Nˆg∗s−closure, Nˆg∗s−boundary andNˆg∗s−border are studied.

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46

S, JACKSON, and GNANAPOO DENOSHA T. "NANO JD CLOSED SETS." Journal of Science and Arts 21, no. 3 (2021): 689–98. http://dx.doi.org/10.46939/j.sci.arts-21.3-a09.

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Nano JD closed sets, a new class of Nano generalized closed sets in Nano topological spaces, relies on the g-interior and g closure operators. This paper aims to interpret and investigate its extension and connection with other existing concepts.

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47

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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48

Bhavani, K. "Generalized locally-$\tau_g\star$-closed sets." Boletim da Sociedade Paranaense de Matemática 35, no. 2 (2017): 171–75. http://dx.doi.org/10.5269/bspm.v35i2.27451.

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In this paper, we define and study a new class of generally locally closed sets called $\I$-locally-$\tau_g^\star$-closed sets in ideal topological spaces. We also discuss various characterizations of $\I$-locally-$\tau_g^\star$-closed sets in terms of $g$-closed sets and $\I_g$-closed sets.

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49

Pestov, V. G. "Absolutely closed sets and a hypothesis of A. A. Markov." Siberian Mathematical Journal 29, no. 2 (1988): 260–66. http://dx.doi.org/10.1007/bf00969738.

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50

Jeyanthi, P., P. Nalayini та Marcelina Mocana. "g* λµ- closed sets in Generalized Topological Spaces". Boletim da Sociedade Paranaense de Matemática 34, № 1 (2016): 203–12. http://dx.doi.org/10.5269/bspm.v34i1.25102.

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Abstract:

In this paper we introduce some new classes of generalized closed sets called *λµ -g-closed, *λµ -g µ -closed and g* λµ -closed sets in generalized topological spaces, which are related to the classes of gµ -closed sets, g-λµ -closed sets and λµ -g-closed sets. We investigate the properties of the newly introduced classes, as well as the connections among the above mentioned classes of generalized closed sets. Also, we give a unified framework for the study of several types of generalized closed sets in a space endowed with two generalized topologies.

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