On strongly \(\theta\)-semi-continuous functions
type: Item
instance of: scholarly article
title: On strongly \(\theta\)-semi-continuous functions
zbMATH Open document ID: 0917.54017
author: Saeid Jafari
author: T. Noiri
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1999-08-02T00:00:00Z
review text: For \((X,\tau)\) a topological space, a subset \(A\) of \(X\) is said to be semi-open if \(A\subset\text{Cl}(\text{Int}(A))\). The complement of a semi-open set is called semi-closed. The intersection of all semi-closed sets containing \(A\) is called the semi-closure of \(A\) and is denoted by \(\text{sCl} (A)\). In this paper the authors introduce a new class of functions called strongly \(\theta\)-semi-continuous functions. A function \(f:X\to Y\) is said to be strongly \(\theta\)-semicontinuous, if for each \(x\in X\) and each open set \(V\) in \(Y\) containing \(f(x)\) there exists a semi-open set \(U\) in \(X\) containing \(x\) such that \(f(\text{sCl}(U))\subset V\). The authors obtain their characterizations and some of their fundamental properties.
Mathematics Subject Classification ID: 54C08
zbMATH DE Number: 1283842
zbMATH Keywords: semi-regular
zbMATH Keywords: semi-\(\theta\)-open
zbMATH Keywords: strongly \(\theta\)-semicontinuous functions
zbMATH Keywords: semi-open set
reviewed by: Valeriu Popa
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1283842