Weak and strong forms of \(\beta\)-irresolute functions
type: Item
instance of: scholarly article
title: Weak and strong forms of \(\beta\)-irresolute functions
zbMATH Open document ID: 1051.54011
DOI: 10.1023/A:1024687630089
author: T. Noiri
published in: Acta Mathematica Hungarica
publication date: 2004-09-07T00:00:00Z
review text: Let \(X\), \(Y\) be topological spaces. A function \(f:X\to Y\) is said to be weakly (resp. strongly) \(\beta\)-irresolute if for each point \(x\in X\) and each semi-preopen subset \(V\subset Y\) containing \(f(x)\), there exists a semi-preopen subset \(U\subset X\) containing \(x\) such that \(f(U)\subset V\cup\text{Int}\, Cl\,\text{Int}\, V\) (resp. \(f(U\cup\text{Int}\, Cl\,\text{Int}\, U)\subset V\)). A subset \(A\) is called semi-preopen if \(A\subset Cl\,\text{Int}\, Cl\, A\). The paper contains various characterizations of the above substitute of continuity and comparisons with other substitutes of similar kind. Semipre-regular spaces are introduced as a natural domain for such functions.
Mathematics Subject Classification ID: 54C08
zbMATH DE Number: 2099062
zbMATH Keywords: semi-preopen
zbMATH Keywords: \(\beta\)-open
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2099062