Abstract

In topology, separation axioms is used to measure how close a topological space is to being metrizable. Spaces that fulfil the axioms are regarded to be nearer to being metrizable than those that do not. In this paper, we introduce new axioms namely $\alpha g$-$\gamma $- regular and $\alpha g$-$\gamma $-normal and analyze their properties in topological spaces. We compare $\alpha g$-$\gamma $- regularity with regularity and $\alpha g$-$\gamma $-normal with normality . Also we obtain the relations between the newly defined spaces and ${\alpha g}_{\gamma }$-${T_i}^{'}(i=0,1,2)$ spaces.

Keywords and Phrases

Topological space, ${\alpha g}_{\gamma }$-open sets, separation axioms, $\alpha g$-$\gamma $-regular, $\alpha g$-$\gamma $-normal.

A.M.S. subject classification

54D15, 54D65, 54F65.

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