On rgwα-Homeomorphism in topological spaces

Abstract

A bijection f: (X, 𝜏) → (Y, σ) is called regular generalized weakly ⍺- homeomorphism if f and f-1 are rgw⍺-continuous. Also we introduce the new class of maps, namely rgw⍺*-homeomorphisms which form a subclass of rgw⍺-homeomorphisms. The class of rgw⍺- homeomorphism and rgw⍺*- homeomorphism maps are closed under composition of maps. We prove that the set of all rgw⍺- homeomorphism and rgw⍺*-homeomorphisms forms a group under the operation composition of maps.