Abstract

Here decomposition of continuity like notion is explored in terms of generalized topology as well as topology on a set. This concept is used as a new tool to study different characterizations of a given generalized topological space, giving a new dimension in the study of topological spaces. Firstly, more properties of $\mu^{*}$-open(closed), $\mu^{'}$-open(closed) sets, $\mu^{'}$-continuous and $~\mu^{*}$-continuous functions are studied. Also, a new family of sets $\mu^{*}_\alpha$-open(closed) and $\mu^{'}_\beta$-open(closed) sets are introduced. In terms of these sets, the notion of $ \mu^{*}_\alpha$-continuous and $\mu^{'}_\beta$-continuous are defined. Interrelations, characterizations of these sets and functions are explored.

Keywords and Phrases

$\mu^{'}$-continuous, $~\mu^{*}$-continuous functions, $\mu^{*}_\alpha$-open, $\mu^{'}_\beta$-open set, $ \mu^{*}_\alpha$-continuous, $\mu^{'}_\beta$-continuous functions.

A.M.S. subject classification

54A05, 54C05.

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