On extension of maps in topological spaces
type: Item
instance of: scholarly article
title: On extension of maps in topological spaces
zbMATH Open document ID: 0664.54009
author: P. Thangavelu
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: In this paper strongly nbd-finite families of subsets of a topological space are introduced and investigated and then used to investigate piecewise definitions of irresolute maps, semi-continuous maps, and semihomeomorphisms. A family \(\{A_ m|\) \(m\in M\}\) of subsets of a space X is strongly nbd-finite if for each \(x\in X\), there is an open set V containing x, satisfying one of the following conditions: (a) \(V\cap A_ m=\emptyset\) for every \(m\in M\), (b) there is a nonempty finite subset N of M such that i) \(V\cap A_ m\neq \emptyset\) for every \(m\in N\), ii) \(V\cap A_ m\subset A_ k\) for every \(m,k\in N\), and iii) \(V\cap A_ m=\emptyset\) for every \(m\not\in N\).
Mathematics Subject Classification ID: 54C10
zbMATH DE Number: 4086512
zbMATH Keywords: semi-open sets
zbMATH Keywords: strongly nbd-finite families
zbMATH Keywords: irresolute maps
zbMATH Keywords: semi- continuous maps
zbMATH Keywords: semihomeomorphisms
reviewed by: Charles Dorsett
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4086512