Locally Beta-closed Spaces
Keywords:
$\beta$-open, $\beta$-closed, $\beta$-regular, $\beta$-$\theta$-open, $\beta$-$\theta$-closed functions, locally $\beta$-closed, locally compact $T_{2}$Abstract
In this paper, we generalize the notion of $\beta$-closedness due to Abd. El-Monsef and Kozae [2] to arbitrary subsets and in terms of it we introduce the class of locally $\beta$-closed spaces and also investigate of its several properties. It is observed that although local $\beta$-closedness is independent of local compact $T_{2}$-ness but one can be obtained from the other by the help of a new class of functions viz. $\beta$-$\theta$-closed functions which are independent not only of closed functions but also of continuous functions.
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