2021
DOI: 10.53570/jnt.896345
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Theory of Generalized Sets in Generalized Topological Spaces

Abstract: Several specific types of generalized sets (briefly, g-Tg-sets) in generalized topological spaces (briefly, Tg-spaces) have been defined and investigated for various purposes from time to time in the literature of Tg-spaces. Our recent research in the field of a new class of g-Tg-sets in Tg-spaces is reported herein as a starting point for more generalized classes. It is shown that the class of g-Tg-sets is a superclass of those whose elements are called open, closed, semi-open, semi-closed, pre-open, pre-clos… Show more

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Cited by 7 publications
(11 citation statements)
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“…Standard references for notations and concepts are [9][10][11][12]. The mathematical structures T def = (Ω, T ) and T g def = (Ω, T g ) , respectively, are T , T g -spaces [9], on both of which no separation axioms are assumed unless otherwise mentioned [4,10].…”
Section: Preliminariesmentioning
confidence: 99%
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“…Standard references for notations and concepts are [9][10][11][12]. The mathematical structures T def = (Ω, T ) and T g def = (Ω, T g ) , respectively, are T , T g -spaces [9], on both of which no separation axioms are assumed unless otherwise mentioned [4,10].…”
Section: Preliminariesmentioning
confidence: 99%
“…is called the class of all g-T g -sets of category ν ∈ I 0 3 (briefly, g-ν-T g -sets) [9,12]. Accordingly, the class of all g-T g -sets [9] are…”
Section: Preliminariesmentioning
confidence: 99%
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“…called T g -connectedness and g-T g -connectedness in T g -spaces (ordinary and generalized connectedness in generalized topological spaces) are no doubt the most important invariant properties [1,2,3]. Indeed, T-connectedness is an absolute property of a T-set [1,4,5], and g-T-connectedness, T g -connectedness and g-T gconnectedness, respectively, are absolute properties of a g-T-set, a T g -set, and a g-T g -set [3,6,7,8,9,10,11]. Typical examples of g-T-connectedness in T -spaces are α, β, γ-connectedness [12,13,14]; examples of T g -connectedness in T g -spaces are semi * α, s, gb-connectedness [2,15,16], whereas examples of g-T g -connectedness in T g -spaces are bT µ , µ-rgb, π p-connectedness [17,18,19], among others.…”
Section: Introductionmentioning
confidence: 99%