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Journal articles on the topic ')*-g-closed set'

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Published: 3 June 2025
Last updated: 31 July 2025

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1

A., Gnana Arockiam, Gilbert Rani M., and Premkumar R. "STRONGLY BINARY G*-CLOSED SET IN BINARY TOPOLOGICAL SPACES." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 07 (2023): 3565–70. https://doi.org/10.5281/zenodo.8174386.

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In  this  paper,  we  introduce  the  concept  of  strongly  binary  g^⋆-closed  sets  in  binary  topological space and we investigate the group of structure of the set of all strongly binary g^⋆-closed sets
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2

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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3

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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4

E., Kungumaraj, and Nirmaladevi K. "Fuzzy Strongly g s Closed sets in Fuzzy Topological spaces." International Journal of Trend in Scientific Research and Development 2, no. 2 (2018): 857–59. https://doi.org/10.31142/ijtsrd9482.

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In this paper, we have introduced and study the concept of strongly g s closed set in Fuzzy topological spaces and discuss some of its properties. E. Kungumaraj | K. Nirmaladevi "Fuzzy Strongly g*s Closed sets in Fuzzy Topological spaces" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-2 , February 2018, URL: https://www.ijtsrd.com/papers/ijtsrd9482.pdf
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5

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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6

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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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

Et.al, Vijayakumari T. "Relations of Pre Generalized Regular Weakly Locally Closed Sets in Topological Spaces." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (2021): 3444–54. http://dx.doi.org/10.17762/turcomat.v12i3.1616.

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In this paper pgrw-locally closed set, pgrw-locally closed*-set and pgrw-locally closed**-set are introduced. A subset A of a topological space (X,t) is called pgrw-locally closed (pgrw-lc) if A=GÇF where G is a pgrw-open set and F is a pgrw-closed set in (X,t). A subset A of a topological space (X,t) is a pgrw-lc* set if there exist a pgrw-open set G and a closed set F in X such that A= GÇF. A subset A of a topological space (X,t) is a pgrw-lc**-set if there exists an open set G and a pgrw-closed set F such that A=GÇF.&#x0D; The results regarding pgrw-locally closed sets, pgrw-locally closed*
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9

Anoche, Jesica, Imelda Aniversario, and Catherine I. Merca. "Path-Induced Closed Geodetic Domination of Some Common Graphs and Edge Corona of Graphs." European Journal of Pure and Applied Mathematics 16, no. 1 (2023): 169–79. http://dx.doi.org/10.29020/nybg.ejpam.v16i1.4506.

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Let G be a connected graph of order n and S ⊆ V (G). A closed geodetic cover S of Gis a path-induced closed geodetic dominating set of a graph G if a subgraph &lt;S&gt; has a Hamiltonianpath and S is a dominating set of G. The minimum cardinality of a path-induced closed geodeticdominating set is called path-induced closed geodetic domination number of G. This study presentsthe characterization of the path-induced closed geodetic dominating sets of some common graphsand edge corona of two graphs. The path-induced closed geodetic domination numbers of thesegraphs are also determined.&#x0D;
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10

A. Devika and R. Vani. "Min-Max $\pi g^* \beta$-continuous and Max-Min $\pi g^* \beta$-continuous functions in topological spaces." Malaya Journal of Matematik 6, no. 03 (2018): 530–35. http://dx.doi.org/10.26637/mjm0603/0011.

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The aim of this paper is to study the notions of minimal $\pi g^* \beta$-closed set, maximal $\pi g^* \beta$-open set, minimal $\pi g^* \beta$-open set, maximal $\pi g^* \beta$-closed set, minimal $\pi g^* \beta$-continuous, maximal $\pi g^* \beta$-continuous, minimal $\pi g^* \beta$ irresolute, maximal $\pi g^* \beta$-irresolute, minimal-maximal $\pi g^* \beta$-continuous and maximal-minimal $\pi g^* \beta$-continuous and their basic properties are studied.
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11

BATAL, Ahmet. "Parity of an odd dominating set." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 71, no. 4 (2022): 1023–28. http://dx.doi.org/10.31801/cfsuasmas.1051208.

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For a simple graph $G$ with vertex set $V(G)=\{v_1,...,v_n\}$, we define the closed neighborhood set of a vertex $u$ as \\$N[u]=\{v \in V(G) \; | \; v \; \text{is adjacent to} \; u \; \text{or} \; v=u \}$ and the closed neighborhood matrix $N(G)$ as the matrix whose $i$th column is the characteristic vector of $N[v_i]$. We say a set $S$ is odd dominating if $N[u]\cap S$ is odd for all $u\in V(G)$. We prove that the parity of the cardinality of an odd dominating set of $G$ is equal to the parity of the rank of $G$, where rank of $G$ is defined as the dimension of the column space of $N(G)$. Usi
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12

Hamja, Jamil, Imelda S. Aniversario, and Helen M. Rara. "On Weakly Connected Closed Geodetic Domination in Graphs Under Some Binary Operations." European Journal of Pure and Applied Mathematics 15, no. 2 (2022): 736–52. http://dx.doi.org/10.29020/nybg.ejpam.v15i2.4356.

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Let G be a simple connected graph. For S ⊆ V (G), the weakly connected closed geodetic dominating set S of G is a geodetic closure IG[S] which is between S and is the set of all vertices on geodesics (shortest path) between two vertices of S. We select vertices of Gsequentially as follows: Select a vertex v1 and let S1 = {v1}. Select a vertex v2 ̸= v1 and let S2 = {v1, v2}. Then successively select vertex vi ∈/ IG[Si−1] and let Si = {v1, v2, ..., vi} for i = 1, 2, ..., k until we select a vertex vk in the given manner that yields IG[Sk] = V (G). Also, the subgraph weakly induced ⟨S⟩w by S is c
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13

Mandal, Dhananjoy, and M. N. Mukherjee. "Certain new classes of generalized closed sets and their applications in ideal topological spaces." Filomat 29, no. 5 (2015): 1113–20. http://dx.doi.org/10.2298/fil1505113m.

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In this paper, a type of closed sets, called *-g-closed sets, is introduced and studied in an ideal topological space. The class of such sets is found to lie strictly between the class of all closed sets and that of generalized closed sets of Levine [5]. We give some applications of *-g-closed set and *-g-open set in connection with certain separation axioms.
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14

Hamant, Kumar Hamant. "Cg-Closed Sets And C-Normal Spaces." International Journal of Creative Research Thoughts (IJCRT) 12, no. 5 (2025): 795–803. https://doi.org/10.5281/zenodo.14872594.

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&nbsp;In this paper, we introduced a new class of sets called C-generalized closed (briefly Cg-closed) set which is a simultaneous generalization of C-closed and g-closed sets. First we investigated basic some properties of Cg-closed sets and then we obtained the relationship of Cg-closed sets with some other existing generalized closed sets. Moreover, we introduced the notion of C-Normal space by using C-closed sets, also we obtained some basic characterizations, properties and preservation theorems of C-normal spaces. Further, we also introduced some function related to Cg-open sets and inve
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15

Parvatkar, Satyamurthy V., and Sadanand N. Patil­. "On Fuzzy strongly g-closed set in Fuzzy Topological Space." International Journal of Advanced Science and Engineering 4, no. 4 (2018): 737. http://dx.doi.org/10.29294/ijase.4.4.2018.737-739.

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16

Meenakumari, N., and T. Indira. "On Decompositions of (r*g*)* Closed Set in Topological Spaces." Annals of Pure and Applied Mathematics 16, no. 1 (2018): 21–30. http://dx.doi.org/10.22457/apam.v16n1a3.

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17

Adolfo, Niña Jeane, Imelda Aniversario, and Ferdinand Jamil. "Closed Geodetic Hop Domination in Graphs." European Journal of Pure and Applied Mathematics 17, no. 3 (2024): 1618–36. http://dx.doi.org/10.29020/nybg.ejpam.v17i3.5241.

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Let G be a simple, undirected and connected graph. A subset S ⊆ V (G) is a geodetic cover of G if IG[S] = V (G), where IG[S] is the set of all vertices of G lying on any geodesic between two vertices in S. A geodetic cover S of G is a closed geodetic cover if the vertices in S are sequentially selected as follows: Select a vertex v1 and let S1 = {v1}. If G is nontrivial, select a vertex v2 ̸= v1 and let S2 = {v1, v2}. Where possible, for i ≥ 3, successively select vertex vi ∈/ IG[Si−1] and let Si = {v1, v2, ..., vi}. Then there exists a positive integer k such that Sk = S. A geodetic cover S o
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18

Powar, P. L., J. K. Maitra та Ramratan Kushwaha. "fγ -PSg-closed sets in Fine Topological Spaces". YMER Digital 21, № 08 (2022): 181–98. http://dx.doi.org/10.37896/ymer21.08/19.

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In this paper, we have defined a new class of sets called fγ-PS-generalized closed sets using fγ-PS-open set and fγ-PS-closure of a set in fine topological space. Also, we have defined some new functions, namely fγ-PS-g-continuous by using the fγ -PS-g-closed set and fγ-PS-g-open set in fine topological space with illustrative examples. AMS Subject Classification: 54XX, 54CXX. Key Words: Fine-open sets, fγ-PS-open sets, fγ-PS-closed sets, fγ-PS-g-continuous function.
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19

S., Devi, Rameshpandi M., and Premkumar R. "Nano weakly g^#-closed sets in nano topological spaces." Asia Mathematika 7, no. 1 (2023): 40——49. https://doi.org/10.5281/zenodo.8074456.

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We define and study the concepts of nano weakly \(g^{\#}\)-closed sets by using the concept of nano \(g^{\#}\)-closed set in nano topological spaces. Further, we discuss the notions such as nano weakly \(g^{\#}\)-continuous functions, nano weakly \(g^{\#}\)-open functions and nano weakly \(g^{\#}\)-closed functions in this paper.
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20

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 &nbsp;&pi;g eta-closed sets in topological spaces and investigate the relationship with other existing&nbsp;generalized closed sets. Moreover, we also study the concepts of &nbsp;&pi;g eta-continuous and almost &nbsp;&pi;g eta-continuous functions in&nbsp;topological spaces. We obtain some properties of&nbsp;&pi;g eta-closed sets and almost &nbsp;&pi;g eta-continuous functions. A subset A of a space&nbsp;(X, ) is said to be g&eta;-closed if &eta;-cl(A)  U whenever A  U and U is -open in X. A function f : X &rarr; Y is called &nbsp;&pi;g eta-&nbsp;continuous if f &m
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21

Zelenyuk, Yevhen. "Closed Left Ideal Decompositions of U(G)." Canadian Mathematical Bulletin 56, no. 2 (2013): 442–48. http://dx.doi.org/10.4153/cmb-2011-175-8.

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AbstractLet G be an infinite discrete group and let βG be the Stone-Čech compactification of G. We take the points of βG to be the ultrafilters on G, identifying the principal ultrafilters with the points of G. The set U(G) of uniform ultrafilters on G is a closed two-sided ideal of βG. For every p ∊ U(G), define Ip ⊆ βG by Ip = ∩ A∊p cl(GU(A)), whereU(A) = {p ∊ U(G) : A ∊ p}. We show that if |G| is a regular cardinal, then {Ip : p ∊ U(G)} is the finest decomposition of U(G) into closed left ideals of βG such that the corresponding quotient space of U(G) is Hausdorff.
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22

N, Gomathi, and Indira T. "Contra Soft g**- Continuous Functions in Soft Topological Spaces." Indian Journal of Science and Technology 16, no. 33 (2023): 2642–48. https://doi.org/10.17485/IJST/v16i33.1487.

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Abstract <strong>Objectives:</strong>&nbsp;The goal of this paper is to introduce the ideas of Contra soft generalized** (briefly Contra soft g**). Continuous functions and almost Contra soft generalized** (briefly almost Contra soft g**) &ndash; Continuous functions in soft topological spaces. Additionally, we discussed some of its characteristics.&nbsp;<strong>Methods:</strong>&nbsp;To obtain the definition of contra soft g**- continuous functions, we used the previously introduced definition(1) (i.e. the inverse image of every soft closed set in FQ is soft g**-closed set in FP). Also, the i
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23

Selvi, G., and I. Rajasekaran. "ON A NEW CLASS OF SEMI GENERALIZED CLOSED SETS IN STRONG GENERALIZED TOPOLOGICAL SPACES." Advances in Mathematics: Scientific Journal 9, no. 11 (2020): 9353–60. http://dx.doi.org/10.37418/amsj.9.11.41.

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This paper deals with the concepts of semi generalized closed sets in strong generalized topological spaces such as $sg^{\star \star}_\mu$-closed set, $sg^{\star \star}_\mu$-open set, $g^{\star \star}_\mu$-closed set, $g^{\star \star}_\mu$-open set and studied some of its basic properties included with $sg^{\star \star}_\mu$-continuous maps, $sg^{\star \star}_\mu$-irresolute maps and $T_\frac{1}{2}$-space in strong generalized topological spaces.
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24

Zhou, Huan, O. G. Hammad, and Ahmed Mostafa Khalil. "On Q p -Closed Sets in Topological Spaces." Journal of Mathematics 2022 (February 18, 2022): 1–10. http://dx.doi.org/10.1155/2022/9352861.

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In the present paper, we will propose the novel notions (e.g., Q p -closed set, Q p -open set, Q p -continuous mapping, Q p -open mapping, and Q p -closed mapping) in topological spaces. Then, we will discuss the basic properties of the above notions in detail. The category of all Q p -closed (resp. Q p -open) sets is strictly between the class of all preclosed (resp. preopen) sets and g p -closed (resp. g p -open) sets. Also, the category of all Q p -continuity (resp. Q p -open ( Q p -closed) mappings) is strictly among the class of all precontinuity (resp., preopen (preclosed) mappings) and
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25

AL-Omeri, Wadei Faris AL. "Neutrosophic G* -Closed Sets in Neutrosophic Topological Spaces." International Journal of Neutrosophic Science 20, no. 4 (2023): 210–22. http://dx.doi.org/10.54216/ijns.200417.

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A neutrosophic set is a mathematical approach that helps with challenges involving data that is indeterminate, imprecise, or inconsistent. The goal of this manuscript is to present the notion of neutrosophic g*-closed sets and neutrosophic g*-open sets. In this situation, we prove various neutrosophic generalized theorems. The findings support previous methodologies in the literature and are backed up by various examples and an application.
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26

BISWAS, REEPA, RAGHAVAN ASOKAN, and MUTHU VINOTH. "STRONGLY NANO (1,2)^⋆-g^⋆-CLOSED SETS IN NANO BITOPOLOGICAL SPACES." Journal of Science and Arts 25, no. 1 (2025): 45–54. https://doi.org/10.46939/j.sci.arts-25.1-a05.

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In this paper, we introduce the concept of strongly nano (1,2)^⋆-g^⋆-closed sets in nano bitopological space and we investigate the group of the structure of the set of all strongly nano (1,2)^⋆-g^⋆-closed sets.
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27

., Kiran G. Potadar, and Sadanand N. Patil . "Comparative Study of Fuzzy *g −Closed Set with other Fuzzy Closed Sets in Fuzzy Topological Spaces." Volume 5 No.3; 2019 5, no. 3 (2019): 1045–51. http://dx.doi.org/10.29294/ijase.5.3.2019.1045-1051.

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28

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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29

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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30

Hamant, Kumar Hamant. "Fg-Closed Sets And F-Normal Spaces." International Journal of Creative Research Thoughts (IJCRT) 12, no. 4 (2025): 577–82. https://doi.org/10.5281/zenodo.14872694.

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&nbsp;In this paper, a new kind of sets called F-generalized closed (briefly Fg-closed) sets are introduced, which is a generalization of F-closed as well as g-closed sets and also studied some basic properties of Fg-closed sets in topological spaces. Further by utilizing Fg-closed sets, we obtained a characterization of normal spaces. &nbsp;Moreover, we also introduced a new class of normal spaces is called F-normal spaces in topological spaces and investigated some properties of F-normal spaces in the terms of Fg-open sets.
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31

S. Sekar and S. Loganayagi. "On generalized b star - closed set in topological Spaces." Malaya Journal of Matematik 5, no. 02 (2017): 401–6. http://dx.doi.org/10.26637/mjm502/018.

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In this paper, we introduce a new class of sets called generalized $b$ star - closed sets in topological spaces (briefly $g b^*$ - closed set). Also we discuss some of their properties and investigate the relations between the associated topology.
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32

Noorani, Mohd Salmi Md. "Closed orbits of(G,τ)-extension of ergodic toral automorphisms". International Journal of Mathematics and Mathematical Sciences 2003, № 17 (2003): 1047–53. http://dx.doi.org/10.1155/s0161171203208164.

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LetA:T→Tbe an ergodic automorphism of a finite-dimensional torusT. Also, letGbe the set of elements inTwith some fixed finite order. Then,Gacts on the right ofT, and by denoting the restriction ofAtoGbyτ, we haveA(xg)=A(x)τ(g)for allx∈Tandg∈G. Now, letA˜:T˜→T˜be the (ergodic) automorphism induced by theG-action onT. Letτ˜be anA˜-closed orbit (i.e., periodic orbit) andτanA-closed orbit which is a lift ofτ˜. Then, the degree ofτoverτ˜is defined by the integerdeg(τ/τ˜)=λ(τ)/λ(τ˜), whereλ( )denotes the (least) period of the respective closed orbits. Suppose thatτ1,…,τtis the distinctA-closed orbit
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33

Kalaivani, P., and R. Nithyakala. "NANO WEAKLY g\# CLOSED MAPS AND NANO WEAKLY g\# OPEN MAPS IN NANO TOPOLOGICAL SPACES." South East Asian Journal of Mathematics and Mathematical Sciences 20, no. 02 (2024): 425–38. https://doi.org/10.56827/seajmms.2024.2002.30.

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The Nano Weakly $g\#$ open set is one of the stronger form of nano topological spaces. In this article we introduce the concept of Nano Weakly $g\#$ open maps and Nano Weakly $g\#$ closed maps in Nano topological spaces and investigate their neighbor maps such as $N\alpha$ open map, $N\alpha g$ open map, $Ng\alpha$ open map, $Nsg$ open map and $Ngs$ open map and their respective nano closed maps in nano topological spaces. Also we analyze some of their related properties.
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34

AL-Jarrah, Heyam H., Amani Rawshdeh, Khalid Y. Al-Zoubi, and Shefa A. Bani Melhem. "On $g \mu$-Paracompact Sets." European Journal of Pure and Applied Mathematics 18, no. 2 (2025): 5899. https://doi.org/10.29020/nybg.ejpam.v18i2.5899.

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In this work, we use the notion of the $g \mu$-paracompact space \cite{ADeb} to introduce two types of $g \mu$-paracompact sets called $\alpha$-$g \mu$-paracompact and $\beta$-$g \mu$-paracompact. We show that every $\alpha$-$g \mu$-paracompact set is $\beta$-$g \mu$-paracompact and if a generalized topological space $(S,\mu)$ is $g \mu$-paracompact, then every $\mu$-closed subset in $(S,\mu)$ is $\alpha$-$g \mu$-paracompact while every $\mu g$-closed subset in $(S, \mu)$ is $\beta$-$g \mu$-paracompact. Finally, we introduce the notion of $co$-$\alpha$-$g\mu$-paracompact set as an application
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35

YADAV, DIWARI LAL, and MANOJ GARG. "New Generalization of Homeomorphism in Topological Spaces." Journal of Ultra Scientist of Physical Sciences Section B 34, no. 1 (2022): 1–5. http://dx.doi.org/10.22147/jusps-b/340101.

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In this paper we introduce a new class of closed maps namely g#s-closed maps also introduce a new class of homeomorphisms called g#s*-homeomorphisms and prove that the set of all g#s*-homeomorphisms form a group under the operation composition of maps.
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36

Alkhazragy, A., A. K. H. Al-Hachami, and F. Mayah. "Notes on Strongly Semi-Closed Graph." Herald of the Bauman Moscow State Technical University. Series Natural Sciences, no. 3 (102) (June 2022): 17–27. http://dx.doi.org/10.18698/1812-3368-2022-3-17-27.

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In these papers, we study on mapping with strongly semi-closed graph. We first introduce the notion "strongly semi-closed graph" in analogue to the closed graph. Also, we study some of their basic properties. This study proved that: If Y is extremally s-disconnected semi-T2-space and f : X → Y is a set-s-connected surjection, then G(f) is semi-closed. If Y is Hausdorff space and f is almost semi continuous, then G(f) is strongly semi-closed. If Y is semi-T2-space and f is irresolute, then G(f) is strongly semi-closed. Semi-closed mapping and semi-closed graph are two separate concepts. If G(f)
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37

Shang, Shaoqiang, and Yunan Cui. "Gateaux Differentiability of Convex Functions and Weak Dentable Set in Nonseparable Banach Spaces." Journal of Function Spaces 2019 (May 2, 2019): 1–12. http://dx.doi.org/10.1155/2019/6852859.

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In this paper, we prove that if C⁎⁎ is a ε-separable bounded subset of X⁎⁎, then every convex function g≤σC is Ga^teaux differentiable at a dense Gδ subset G of X⁎ if and only if every subset of ∂σC(0)∩X is weakly dentable. Moreover, we also prove that if C is a closed convex set, then dσC(x⁎)=x if and only if x is a weakly exposed point of C exposed by x⁎. Finally, we prove that X is an Asplund space if and only if, for every bounded closed convex set C⁎ of X⁎, there exists a dense subset G of X⁎⁎ such that σC⁎ is Ga^teaux differentiable on G and dσC⁎(G)⊂C⁎. We also prove that X is an Asplund
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38

AL-SHARIF, SH. "On farthest and simultaneous farthest points in Kothe spaces." Creative Mathematics and Informatics 21, no. 2 (2012): 123–28. http://dx.doi.org/10.37193/cmi.2012.02.10.

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Let X be a real Banach space and G be a closed bounded subset of X. For x e X, we set ρ (x, G) = sup {kx − yk : y e G} . The set G is called remotal if for any x e X, there exists g e G such that ρ (x, G) = kx − gk . In this paper we show that for a separable remotal set G ⊂ X, the set E(G) is remotal in E(X), where E(X) is the Kothe Bochner function space. Some other results are presented.
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39

KEARNES, KEITH A., and ÁGNES SZENDREI. "CLONES CLOSED UNDER CONJUGATION I: CLONES WITH CONSTANTS." International Journal of Algebra and Computation 18, no. 01 (2008): 7–58. http://dx.doi.org/10.1142/s0218196708004251.

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We show that if G ≤ S A is a permutation group on a finite set A satisfying |A| ≥ 3, then the set of G-closed clones on A that contain all constant operations is finite iff G = S A, A A, AGL(1,5) (|A| = 5), PSL(2,5) (|A| = 6), PGL(2,5) (|A| = 6), PGL(2,7) (|A| = 8), PGL(2,8) (|A| = 9), or PΓL(2,8) (|A| = 9).
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40

R. Navalakhe. "Generalized Fuzzy Continuous Maps and Generalized Fuzzy Closed Maps in Fuzzy Biclosure Space." International Journal of Fuzzy Mathematical Archive 19, no. 01 (2021): 81–94. http://dx.doi.org/10.22457/ijfma.v19n1a06228.

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The aim of this paper is to introduce the notion of generalized fuzzy continuous maps and generalized fuzzy closed maps in fuzzy biclosure spaces by using the concept of generalized fuzzy closed set briefly a g -fuzzy closed set. In this paper study and investigation of some important properties and characterizations of generalized fuzzy continuous maps and generalized fuzzy closed maps in fuzzy biclosure spaces has also been done.
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41

Sooryanarayana, Badekara, and Suma Agani Shanmukha. "Graphs of Neighborhood Metric Dimension Two." Journal of Mathematical and Fundamental Sciences 53, no. 1 (2021): 118–33. http://dx.doi.org/10.5614/j.math.fund.sci.2021.53.1.9.

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A subset of vertices of a simple connected graph is a neighborhood set (n-set) of G if G is the union of subgraphs of G induced by the closed neighbors of elements in S. Further, a set S is a resolving set of G if for each pair of distinct vertices x,y of G, there is a vertex s∈ S such that d(s,x)≠d(s,y). An n-set that serves as a resolving set for G is called an nr-set of G. The nr-set with least cardinality is called an nr-metric basis of G and its cardinality is called the neighborhood metric dimension of graph G. In this paper, we characterize graphs of neighborhood metric dimension two.
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42

Granirer, Edmond E. "Amenability and semisimplicity for second duals of quotients of the Fourier algebraA(G)." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 63, no. 3 (1997): 289–96. http://dx.doi.org/10.1017/s1446788700000938.

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AbstractLetF ⊂ Gbe closed andA(F) = A(G)/IF. IfFis a Helson set thenA(F)**is an amenable (semisimple) Banach algebra. Our main result implies the following theorem: LetGbe a locally compact group,F ⊂ Gclosed,a ∈ G. Assume either (a) For some non-discrete closed subgroupH, the interior ofF ∩ aHinaHis non-empty, or (b)R ⊂ G, S ⊂ Ris a symmetric set andaS ⊂ F. ThenA(F)**is a non-amenable non-semisimple Banach algebra. This raises the question: How ‘thin’ canFbe forA(F)**to remain a non-amenable Banach algebra?
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43

Aull, C. E. "Some embeddings related to C*-embeddings." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 44, no. 1 (1988): 88–104. http://dx.doi.org/10.1017/s1446788700031396.

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AbstractA space S is R*-embedded (G*-embedded) in a space X if two disjoint regular closed sets (closure disjoint open sets) of S are contained in disjoint regular closed sets (extended to closure disjoint open sets) of X. A space S is R-extendable to a space X if any regular closed set of S can be extended to a regular closed set of X. It is shown that R*-embedding and G*-embedding are identical with C*-embedding for certain fairly general classes of Tychonoff spaces. Under certain conditions it is shown that R-extendability is related to z-embedding. Spaces in which the regular open sets are
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44

SHUMYATSKY, PAVEL. "ELEMENTS OF PRIME POWER ORDER IN RESIDUALLY FINITE GROUPS." International Journal of Algebra and Computation 15, no. 03 (2005): 571–76. http://dx.doi.org/10.1142/s0218196705002384.

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45

Taha, I. M. "On r -Generalized Fuzzy ℓ -Closed Sets: Properties and Applications". Journal of Mathematics 2021 (27 грудня 2021): 1–8. http://dx.doi.org/10.1155/2021/4483481.

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In the present study, we introduce and characterize the class of r -generalized fuzzy ℓ -closed sets in a fuzzy ideal topological space X , τ , ℓ in Šostak sense. Also, we show that r -generalized fuzzy closed set by Kim and Park (2002) ⟹ r -generalized fuzzy ℓ -closed set, but the converse need not be true. Moreover, if we take ℓ = ℓ 0 , the r -generalized fuzzy ℓ -closed set and r -generalized fuzzy closed set are equivalent. After that, we define fuzzy upper (lower) generalized ℓ -continuous multifunctions, and some properties of these multifunctions along with their mutual relationships ar
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46

Hamant, Kumar Hamant. "pigeta-CLOSED SETS IN BITOPOLOGICAL SPACES." EPRA International Journal of Research and Development (IJRD) 7, no. 6 (2022): 313–20. https://doi.org/10.5281/zenodo.14880980.

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In this paper, a new class of sets namely pig&eta;-closed, pig&eta;-closure of a set and pig&eta;-neighbourhood in bitopological spaces are introduced and some of their basic properties are discussed. The relationships among closed, alpha-closed, s-closed, &eta;closed, g&eta;-closed and other generalized closed sets are investigated. Several examples are provided to illustrate the behavior of these new class of sets.
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47

Hamrouni, Hatem, and Bilel Kadri. "Locally compact groups with totally disconnected space of subgroups." Journal of Group Theory 22, no. 1 (2019): 119–32. http://dx.doi.org/10.1515/jgth-2018-0034.

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Abstract The closed subsets {\mathcal{F}(X)} of any topological space can be given a topology, called the Chabauty–Fell topology, in which {\mathcal{F}(X)} is quasi-compact. If X is a locally compact space, then {\mathcal{F}(X)} is Hausdorff. If {X=G} is a locally compact group, then the subset {\mathcal{S\kern-0.853583ptU\kern-0.569055ptB}(G)} of closed subgroups is closed in {\mathcal{F}(G)} , and the set of closed subgroups inherits its own compact topology, called the Chabauty topology. We develop some of the important properties of this topology. More precisely, the results contained in t
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48

Skiba, Alexander N. "On some classes of sublattices of the subgroup lattice." Journal of the Belarusian State University. Mathematics and Informatics, no. 3 (November 29, 2019): 35–47. http://dx.doi.org/10.33581/2520-6508-2019-3-35-47.

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In this paper G always denotes a group. If K and H are subgroups of G, where K is a normal subgroup of H, then the factor group of H by K is called a section of G. Such a section is called normal, if K and H are normal subgroups of G, and trivial, if K and H are equal. We call any set S of normal sections of G a stratification of G, if S contains every trivial normal section of G, and we say that a stratification S of G is G-closed, if S contains every such a normal section of G, which is G-isomorphic to some normal section of G belonging S. Now let S be any G-closed stratification of G, and l
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49

SANKI, BIDYUT. "SYSTOLIC FILLINGS OF SURFACES." Bulletin of the Australian Mathematical Society 98, no. 3 (2018): 502–11. http://dx.doi.org/10.1017/s0004972718000862.

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A filling of a closed hyperbolic surface is a set of simple closed geodesics whose complement is a disjoint union of hyperbolic polygons. The systolic length is the length of a shortest essential closed geodesic on the surface. A geodesic is called systolic, if the systolic length is realised by its length. For every $g\geq 2$, we construct closed hyperbolic surfaces of genus $g$ whose systolic geodesics fill the surfaces with complements consisting of only two components. Finally, we remark that one can deform the surfaces obtained to increase the systole.
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50

Weiss, Richard. "A uniqueness lemma for groups generated by 3-transpositions." Mathematical Proceedings of the Cambridge Philosophical Society 97, no. 3 (1985): 421–31. http://dx.doi.org/10.1017/s030500410006299x.

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Let G be a group. A subset D of G will be called a set of 3-transpositions if |x| =2 for all xεD and |xy| = 3 whenever x, yεD do not commute. We will call the set D closed if xDx = D for each xεD. For each xεD, let
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