On a Class of Sets Via Grill : A Decomposition of Continuity

Abstract

In the present article, a class of sets, called Ϟ-semiclosed sets, which is a subclass of the class of semi-closed sets of Levine [7], is introduced and studied in a grill topological space (X, τ, Ϟ), where Ϟ is a grill on X. Two types of functions are then introduced which ultimately lead us to achieve a new decomposition of a continuous function

Keywords

• grill
• semi-open set
• ϟ-semiopen set
• ϟ-semicontinuity
• ϟs-set
• ϟs-continuity