On \(\theta\)-generalized closed sets
type: Item
instance of: scholarly article
title: On \(\theta\)-generalized closed sets
zbMATH Open document ID: 0927.54037
DOI: 10.1155/S0161171299222399
author: Julian Dontchev
author: H. Maki
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1999-12-13T00:00:00Z
full work available at URL: https://eudml.org/doc/48306
review text: A subset \(A\) of a topological space \(X\) is called \(\theta\)-closed, if \(A=\text{cl}_\theta (A)\) where \(\text{cl}_\theta(A)= \{x\in X: \text{cl} (U)\cap A\neq\emptyset\) for each open neighbourhood \(U\) of \(x\}\). In this paper the authors consider a new class of subsets, namely \(\theta\)-generalized closed sets, i.e. subsets \(A\) where \(\text{cl}_\theta (A) \subseteq U\) whenever \(A\subseteq U\) and \(U\) is open. They establish basic properties of this class of subsets, in particular they point out that this class is placed properly between the classes of generalized closed sets (in the sense of Levine) and \(\theta\)-closed sets. In the subsequent sections of the paper, \(\theta\)-\(g\)-continuous and \(\theta\)-\(g\)-irresolute functions are introduced and investigated. Moreover, the property ``TGO-connected'' is introduced and the behaviour of this type of connectedness under various mappings is exhibited.
Mathematics Subject Classification ID: 54H05
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 54D10
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54D99
zbMATH DE Number: 1334830
zbMATH Keywords: \(\theta\)-closure
zbMATH Keywords: \(\theta\)-generalized closed sets
zbMATH Keywords: TGO-connected
reviewed by: Maximilian Ganster
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1334830