Applications of pre-open sets

Abstract

Using the concept of pre-open set, we introduce and study topological properties of pre-limit points, pre-derived sets, preinterior and pre-closure of a set, pre-interior points, pre-border, prefrontier and pre-exterior. The relations between pre-derived set (resp. pre-limit point, pre-interior (point), pre-border, pre-frontier, and preexterior) and α-derived set (resp. α-limit point, α-interior (point), α-border, α-frontier, and α-exterior) are investigated.

Keywords

• Pre-limit point
• Pre-derived set
• Pre-interior
• Pre-closure
• Pre-interior points
• Pre-border
• Pre-frontier
• Pre-exterior