Applications of pre-open sets

Young Bae Jun, Seong Woo Jeong, Hyeon Jeong Lee, Joon Woo Lee

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

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Universitat Politècnica de València

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