Between closed and Ig-closed sets

Néstor Raúl Pachón

Abstract

The concept of closed sets is a central object in general topology. In order to extend many of important properties of closed sets to a larger families, Norman Levine initiated the study of generalized closed sets. In this paper we introduce, via ideals, new generalizations of closed subsets, which are strong forms of the Ig-closed sets, called ρIg-closed sets and closed-I sets. We present some properties and applications of these new sets and compare the ρIg-closed sets and the closed-I sets with the g-closed sets introduced by Levine. We show that Iclosed and closed-I are independent concepts, as well as I∗-closed sets and closed-I concepts.

Keywords

g-closed sets, C-compact spaces, I-compact spaces

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