New Topologies From Obtained Operators via Weak Semi-Local Function, and Some Comparisons

Abstract

In this paper, the local function, the weak semi-local function and the local closure function are compared with each other according to the inclusion relation. We define a new operator by using the weak semi-local function and investigate its properties. Thanks to this operator, we obtain two new topologies which finer than some previously defined topologies. Finally, locally countable spaces are characterized by
the local function.