On s*g-alpha-Proper Functions

Abstract

In this paper we introduce a new class of  functions  in topological spaces, namely, s*g-?-proper functions. Also,  we  study  the basic properties and characterizations of  these functions. One of the most  important of equivalent definitions to the s*g-?-proper functions gives by using s*g-?-limit points of nets. Moreover we define and study s*g-?-perfect functions and s*g-?-compact functions in topological spaces and  we  study  the relation  between  s*g-?-proper functions  and  each of proper functions, s*g-?-perfect functions, closed functions, s*g-?-closed functions and s*g-?-compact  functions and we give an example when the converse may not be true.

Key words: s*g-?-proper  functions,  s*g-?-perfect  functions, s*g-?-closed  functions,  s*g-?-compact functions, s*g-?-limlt points, compactly s*g-?-closed sets and s*g-?-K-spaces.