On theta-connectedness and theta-closure spaces

Abstract

Let (X, T) be a topological space. A point x is in the theta-closure of A, denoted by cl(theta) A, if each closed neighbourhood of x intersects A. The pair (X, cltheta) is a closure space, also called a neighbourhood space. A subset A is theta-closed if A = cl(theta) A. theta-closed sets are closed sets for a new topology To on the set X. The semi-regularization topology of T is denoted by T-s. Various topological properties are considered on (X, T), (X, T-s), (X, cl(theta)) and (X, T-theta), in particular connectedness and local connectedness.