Abstract
Let (X, T ) be a topological space. A point x is in the θ-closure of A, denoted by cl θ A, if each closed neighbourhood of x intersects A. The pair ( X,cl θ ) is a closure space, also called a neighbourhood space. A subset A is θ-closed if A=cl θ A. θ-closed sets are closed sets for a new topology T θ 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 θ) and (X, T θ) , in particular connectedness and local connectedness.
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