On θ-connectedness and θ-closure spaces

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