Some Generalized Results on $G_{\delta} $-diagonal Regular Spaces

Abstract

In this paper we constructed a space X possessing a regular $G_{\delta}$-diagonal set of full measure, then the space X has a diagonal set if $\{(x,x):x\in X\} $ and is regular in $G_{\delta}-set$ for $X\times X$. We extend our result for some characterization of spaces with $G_{\delta }$-diagonal set. Such a kind obtained by Borges.C.J.R [1], Cinder.J.G [2] and Zenor.P [5].