Locally Beta-closed Spaces (European Journal of Pure and Applied Mathematics, 2009)
In this paper, we generalize the notion of $β$-closedness due to Abd. El-Monsef and Kozae [2] to arbitrary subsets and in terms of it we introduce the class of locally $β$-closed spaces and also investigate of its several properties. It is observed that although local $β$-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. $β$-$θ$-closed functions which are independent not only of closed functions but also of continuous functions.