Expansion of open sets and decomposition of continuous mappings
type: Item
instance of: scholarly article
title: Expansion of open sets and decomposition of continuous mappings
zbMATH Open document ID: 0818.54009
DOI: 10.1007/BF02844844
publication date: 1995-06-01T00:00:00Z
review text: For a topological space \((X, \tau)\) a mapping \(\Phi: X\to 2^ X\) is called an expansion on \(X\) if \(U\subseteq \Phi(U)\) for each \(U\in \tau\). Using this concept the author defines \(\Phi\)-expansion continuous mappings between topological spaces which enables him to provide a very general decomposition of continuity. As a corollary he obtains the well known result that a mapping between two topological spaces is continuous if and only if it is weakly continuous and weak* continuous.
Mathematics Subject Classification ID: 54C05
zbMATH DE Number: 760332
zbMATH Keywords: expansion
zbMATH Keywords: decomposition of continuity
author: Jing Cheng Tong
reviewed by: Maximilian Ganster
MaRDI profile type: Publication
cites work: Some Remarks on Weak Continuity
cites work: Remarks on Two Weak Forms of Continuity
cites work: A Decomposition of Continuity in Topological Spaces
cites work: On Weakly Continuous Mappings
cites work: Weak-continuity and closed graphs
cites work: On Levine′s Decomposition of Continuity
cites work: A decomposition of continuity
cites work: On decomposition of continuity in topological spaces
published in: Rendiconti del Circolo Matematico di Palermo
Recommended article: Expansion of \(\alpha\)-open sets and decomposition of \(\alpha\)-continuous mappings
Recommended article: Q4832604
Recommended article: Q4955582
Recommended article: Extensions of compact continuous maps into decomposable sets
Recommended article: Expansion of Open Sets in Ideal Topological Spaces
Recommended article: Q3475977
Recommended article: Q3457374
Recommended article: Enlargements of Almost Open Mappings
Recommended article: Q4017432
Recommended article: Tychonoff expansions in which a given set is open
description: scientific article; zbMATH DE number 760332