A note on wβ-open sets on weak spaces

초록

This note is to introduce the notion of wβ-open set in w-spaces, which is a generalization of w-open sets. We study some basic properties of such the notion and figure out the relations among w-semi-open sets, w-preopen sets and wβ-open sets. Moreover, we characterize the weak W-continuity in terms of wβ-open sets. In fact, for a function f:(X, w<inf>X</inf>) → (Y, w<inf>Y</inf>) in w-spaces X and Y, if the w-space Y has the operator preserving property (OPP), then f is a weakly W-continuous function if and only if wC(f -1(wI(wC(G)))) ⊆ f -1(wC(G)) for every β-open set G of Y. © 2016 Pushpa Publishing House, Allahabad, India.

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