New separation axioms in generalized topological spaces
type: Item
instance of: scholarly article
title: New separation axioms in generalized topological spaces
zbMATH Open document ID: 1249.54007
published in: Acta Mathematica Hungarica
publication date: 2011-12-20T00:00:00Z
review text: A family \(\mu\) of subsets of a set \(X\) is called a general topology on \(X\) if \(\mu\) is closed under arbitrary unions and \(\emptyset\in\mu\). All these \((X,\mu)\)'s are called generalized topological spaces (briefly, GTS), as generalizations of topological spaces. The T\(_0\)- and T\(_1\)-separation axioms can be similarly defined in generalized topological spaces as in topological spaces, called \(\mu\)-T\(_0\) and \(\mu\)-T\(_1\), respectively. In this paper, the author introduces some new separation axioms lying between \(\mu\)-T\(_0\) and \(\mu\)-T\(_1\) in generalized topological spaces, namely, \(\mu\)-T\(_{\frac{1}{2}}\), \(\mu\)-T\(_{\frac{1}{4}}\) and \(\mu\)-T\(_{\frac{3}{8}}\). Some characterizations of these separation axioms are given. Also the author discusses the relations between these new separation axioms and some of other ones in GTSs.
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54A10
Mathematics Subject Classification ID: 54D10
zbMATH DE Number: 5990897
zbMATH Keywords: generalized topological spaces
zbMATH Keywords: separation axioms
zbMATH Keywords: \(\mu\)-T\(_{\frac{1}{2}}\)
zbMATH Keywords: \(\mu\)-T\(_{\frac{1}{4}}\)
zbMATH Keywords: \(\mu\)-T\(_{\frac{3}{8}}\)
author: Mohammad S. Sarsak
reviewed by: Shou Lin
MaRDI profile type: Publication
full work available at URL: s10474-010-0066-y
OpenAlex ID: W1992117499
cites work: Generalized topology, generalized continuity
cites work: Generalized open sets in generalized topologies
cites work: Further remarks on the formula for \(\gamma\)-interior
cites work: Remarks on quasi-topologies
cites work: Weak separation axioms in generalized topological spaces
DOI: 10.1007/S10474-010-0066-Y
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description: scientific article; zbMATH DE number 5990897