(untitled) (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.