Remarks on generalized hyperconnectedness
type: Item
instance of: scholarly article
title: Remarks on generalized hyperconnectedness
zbMATH Open document ID: 1265.54022
published in: Acta Mathematica Hungarica
publication date: 2012-09-17T00:00:00Z
review text: Results include the following: Theorem 1. Let \((X, \mu)\) be a strong generalized topological space. The following conditions are equivalent: (a) \(X\) is hyperconnected. (b) \(c_{\beta} (U) = X\) for every non empty semi open set \(U\), where \(c_{\beta}\) denotes the \(\beta\)-closure. (c) \(c_\pi (U) = X\) for every non empty semi open set \(U\) where \(\pi\) =\{all preopen sets\}. Theorem 2. Let \((X, \mu)\) be a generalized topological space. If \(X\) is \(\beta\)-connected, then \(X\) is \(\pi\)-irreducible. Theorem 3. Let \((X, \mu)\) be an extremally disconnected generalized topological space. Then \(X\) is strong. Theorem 4. Let \((X, \mu)\) be a strong space. If \(X\) is hyperconnected, then \(X\) is extremally disconnected. There is also a section dealing with embedding into hyperconnected spaces.
reviewed by: K. Chandrasekhara Rao
Mathematics Subject Classification ID: 54A05
Mathematics Subject Classification ID: 54D10
zbMATH DE Number: 6083189
zbMATH Keywords: generalized topology
zbMATH Keywords: \(\mu\)-open
zbMATH Keywords: \(\mu\)-closed
zbMATH Keywords: \(\mu r\)-open
zbMATH Keywords: \(\mu r\)-closed and \(\mu\)-rare sets
zbMATH Keywords: generalized hyperconnected
zbMATH Keywords: extremally disconnected and strong spaces
author: V. Renukadevi
MaRDI profile type: Publication
full work available at URL: s10474-011-0192-1
OpenAlex ID: W2094504631
cites work: Generalized open sets
cites work: On the \(\gamma\)-interior and \(\gamma\)-closure of a set
cites work: Generalized topology, generalized continuity
cites work: \(\gamma\)-connected sets
cites work: Q3373896
cites work: Generalized open sets in generalized topologies
cites work: \(\delta\)- and \(\theta\)-modifications of generalized topologies
cites work: Product of the generalized topologies
cites work: Generalized hyperconnectedness
cites work: On \(\gamma\)-semi-open sets
cites work: \(D\)-sets and decompositions of continuity in generalized topological spaces
cites work: A note on generalized connectedness
DOI: 10.1007/S10474-011-0192-1
description: scientific article; zbMATH DE number 6083189