Abstract

Weak structure space (briefly, wss) has master looks, when the whole space is not open, and these classes of subsets are not closed under arbitrary unions and finite intersections, which classify it from typical topology. Our main target of this article is to introduce psi _{{mathcal {H}}}(.)-operator in hereditary class weak structure space (briefly, {mathcal {H}}wss) (X, w, {mathcal {H}}) and examine a number of its characteristics. Additionally, we clarify some relations that are credible in topological spaces but cannot be realized in generalized ones. As a generalization of w-open sets and w-semiopen sets, certain new kind of sets in a weak structure space via psi _{{mathcal {H}}}(.)-operator called psi _{{mathcal {H}}}-semiopen sets are introduced. We prove that the family of psi _{{mathcal {H}}}-semiopen sets composes a supra-topology on X. In view of hereditary class {mathcal {H}}_{0}, w T_{1}-axiom is formulated and also some of their features are investigated.

Highlights

  • Various topics have been initiated as a result of the interaction between topology and life’s problems [1, 2]

  • The characterizations of the hereditary classes idea H on a nonempty set X, S ∈ H and S ⊂ S implies S ∈ H, which was created by Csaszar in [3], are applicable

  • In [4], Csaszar inserted the notion of weak structures w on X that is usable in digital topology

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Summary

Introduction

Various topics have been initiated as a result of the interaction between topology and life’s problems [1, 2]. We give an example to show that the reverse inclusion of Theorem 5 (2) fails to hold in general: Consider w = {∅, {d}, {a, b}, {b, c}} is a weak structure on X = {a, b, c, d} with a hereditary class H = {∅, {c}, {d}} . Definition 4 If N, S are w-open, w-closed sets, respectively, and N \ S ∈ H implies N ⊂ S , a hereditary class H is said to be strongly w-codense on (X, w). Theorem 9 Let w be closed under finite intersection and a hereditary class H be strongly w-codense on X.

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