On Gα -open sets

Abstract

The new concepts in grill topological spaces are investigated in this study by employing specified sets in which the α-open sets are defined and grill topological spaces. Properties of this set and certain relationships are studied, examining a group of functions, like open, closed, and continuous functions, determining their relation with each other and giving examples and properties associated with this set. This shall serve as the beginning of examining numerous topological properties with this set.