Real-valued functions and some related spaces
type: Item
instance of: scholarly article
title: Real-valued functions and some related spaces
zbMATH Open document ID: 1393.54006
author: Er-Guang Yang
published in: Topology and its Applications
publication date: 2018-03-16T00:00:00Z
review text: Several properties of a topological space \(X\) are characterized in terms of continuous, upper semi-continuous and lower semi-continuous mappings from \(X\) into the unit closed segment \([0,1]\). The following properties are characterized: metrizability, (strong) first countability, ultrametrizability, semi-metrizability, \(o\)-semi-metrizabity, \(K\)-semi-metrizability, (strong) quasi-metrizability, developability, and also \(\sigma\)-space, \(\gamma\)-space and Nagata space properties.
Mathematics Subject Classification ID: 54C30
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 54E20
Mathematics Subject Classification ID: 54E25
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 6851256
zbMATH Keywords: real-valued functions
zbMATH Keywords: \(g\)-functions
zbMATH Keywords: first countable spaces
zbMATH Keywords: \(\gamma\)-spaces
zbMATH Keywords: Nagata spaces
zbMATH Keywords: semi-metric spaces
zbMATH Keywords: quasi-metric spaces
zbMATH Keywords: metric spaces
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
full work available at URL: j.topol.2018.02.007
OpenAlex ID: W4206041996
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DOI: 10.1016/J.TOPOL.2018.02.007
description: scientific article; zbMATH DE number 6851256