An Extension of Semi-Open Sets with Applications on Spaces, Functions : Topological Space

The aim of this work is to introduce and study a new class of set as an extension of semi-open sets in topological spaces called the Sw-open set. We use this set to define new types of continuous functions and new types of topological spaces.It is proved that every Sw-open set is dense and both the families SwO(X) and SO(X) coincide whenever the space X is hyperconnected. The topological spaces (X, ) and (X, ) have the same family of Sw-open sets.The concept of Sw-compactness is introduced and we prove that a space X is Sw-compact if and only if for every somewhat preopen cover of a space X there is a finite subcover under the condition that X is strongly irresolvable.Separation axioms are defined and characterized and it is proved that the space X is Sw-T2 whenever each point of X possesses an Sw-regular subset which is an Sw-T2 subspace in X.