Open AccessBetween closed and Ig-closed sets
Author(s) -
Néstor Raúl Pachón
Publication year - 2018
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v11i2.3131
Subject(s) - closed set , mathematics , closed form expression , set (abstract data type) , open and closed maps , object (grammar) , discrete mathematics , pure mathematics , computer science , mathematical analysis , artificial intelligence , programming language
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 ÏIg-closed sets and closed-I sets. We present some properties and applications of these new sets and compare the ÏIg-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.