Some separation axioms in generalized topological spaces

Pankajam, V.; Sivaraj, D.

doi:10.5269/bspm.v31i1.12969

Cited by 5 publications

(3 citation statements)

References 14 publications

(19 reference statements)

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“…. ), founded upon the concepts of T g , g-T g -open sets, have been introduced and studied [9,10,11,12,13,14,15,16]. The T α -axioms called T Kolmogorov , T Frchet , T Hausdorff , T Regular , and T Normal -axioms (shortly, T K , T F , T H , T R , and T N ), founded upon the concepts of T -open, closed sets, are four classical examples, among others, which have gained extensive studies [17].…”

Section: Introductionmentioning

confidence: 99%

Theory of Generalized Separation Axioms in Generalized Topological Spaces

KHODABOCUS

Sookia

2022

Journal of Universal Mathematics

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In this paper, a new class of generalized separation axioms (briefly, g-Tg-separation axioms) whose elements are called g-T g,K , g-T g,F , g-T g,H , g-T g,R , g-T g,N -axioms is defined in terms of generalized sets (briefly, g-Tg-sets) in generalized topological spaces (briefly, Tg-spaces) and the properties and characterizations of a Tg-space endowed with each such g-T g,K , g-T g,F , g-T g,H , g-T g,R , g-T g,N -axioms are discussed. The study shows that g-T g,F -axiom implies g-T g,K -axiom, g-T g,H -axiom implies g-T g,F -axiom, g-T g,R -axiom implies g-T g,H -axiom, and g-T g,N -axiom implies g-T g,R -axiom. Considering the T g,K , T g,F , T g,H , T g,R , T g,N -axioms as their analogues but defined in terms of corresponding elements belonging to the class of open, closed, semi-open, semiclosed, preopen, preclosed, semi-preopen, and semi-preclosed sets, the study also shows that the statement Tg,α-axiom implies g-T g,α -axiom holds for each α ∈ {K, F, H, R, N}. Diagrams expose the various implications amongst the classes presented here and in the literature, and a nice application supports the overall theory.

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Section: Introductionmentioning

confidence: 99%

Theory of Generalized Separation Axioms in Generalized Topological Spaces

KHODABOCUS

Sookia

2022

Journal of Universal Mathematics

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“…After Császár [6] gave the notions of generalized topological space and generalized neighborhood systems in 2002, many topologists applied the concepts in general topology to the generalized topological spaces: separation axioms in generalized topologies, product of generalized topologies, generalized continuity, generalized compactness, generalized connectedness, etc. [1,7,8,10,14,16] This topological concept was combined with algebra in 2013 by Hussain and et al [12]. They have defined a generalized topological group as a group endowed with a generalized topology such that the multiplication and inversion of the group are generalized continuous according to this generalized topology.…”

Section: Introductionmentioning

confidence: 99%

Generalized Topological Groupoids

Gürsoy

2021

Punjab Univ. j. math.

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Our aim in this paper is to give the notion of generalized topological groupoid which is a generalization of the topological groupoid by using the notion of generalized topology defined by Csasz ´ ar [6]. We in- ´ vestigate the basic facts in the groupoid theory in terms of generalized topological groupoids. We present the action of a generalized topological groupoid on a generalized topological space. We obtain some characterizations about this concept that is called the generalized topological action. Beside these, we give definition of a generalized topological crossed module by generalizing the concept of crossed module defined on topological groupoids. At the last part of the study, we show how a generalized topological crossed module can be obtained from a generalized topological groupoid and how a generalized topological groupoid can be obtained from a generalized topological crossed module.

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“…. ), founded upon the concepts of T g , g-T g -open sets, have been introduced and studied [1,9,11,12,13,20,22]. The T α -axioms called T Kolmogorov , T Fréchet , T Hausdorff , T Regular , and T Normal -axioms (shortly, T K , T F , T H , T R , and T N ), founded upon the concepts of T -open, closed sets, are four classical examples, among others, which have gained extensive studies [27].…”

Section: Introductionmentioning

confidence: 99%

Theory of g-Tg-Separation Axioms

Khodabocus¹,

Sookia²

2018

Preprint

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Abstract. Several specific types of ordinary and generalized separation axioms of a generalized topological space have been defined and investigated for various purposes from time to time in the literature of topological spaces. Our recent research in the field of a new class of generalized separation axioms of a generalized topological space is reported herein as a starting point for more generalized classes.

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Some separation axioms in generalized topological spaces

Abstract: We give different definitions for g-closed sets, R 0 and R 1 spaces in generalized topological spaces, characterize such spaces and compare with the existing definitions and results.

Cited by 5 publications

References 14 publications

Theory of Generalized Separation Axioms in Generalized Topological Spaces

Theory of Generalized Separation Axioms in Generalized Topological Spaces

Generalized Topological Groupoids

Theory of g-Tg-Separation Axioms

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