On the density of the space of continuous and uniformly continuous functions
type: Item
instance of: scholarly article
title: On the density of the space of continuous and uniformly continuous functions
zbMATH Open document ID: 1088.54009
author: Camillo Costantini
published in: Topology and its Applications
publication date: 2006-03-20T00:00:00Z
review text: In this paper the density of function spaces is discussed. For \(X\) a metrizable space and \((Y, \rho)\) a metric space, with \(Y\) pathwise connected, the author computes the density of the spaces \((C(X, (Y, \rho)), \sigma)\) of all continuous functions, and of the spaces \((UC((X, d), (Y, \rho), \sigma)\) of all uniformly continuous functions endowed with the supremum metric \(\sigma\). To carry out this investigation out, the notions of generalized compact and generalized totally bounded metric space turn out to play an important role.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54C05
zbMATH DE Number: 5013523
zbMATH Keywords: density
zbMATH Keywords: extent
zbMATH Keywords: metric space
zbMATH Keywords: continuous function
zbMATH Keywords: uniformly continuous function
zbMATH Keywords: function space
reviewed by: Shou Lin
MaRDI profile type: Publication
full work available at URL: j.topol.2005.03.002
OpenAlex ID: W2091538619
cites work: Q4383408
cites work: Q4227930
cites work: Which Connected Metric Spaces are Compact?
cites work: Q4060144
cites work: Q3994935
cites work: Topological Completions of Metrizable Spaces
cites work: Coarser connected topologies
cites work: Q5185667
cites work: Q3852172
cites work: Q5630317
cites work: Q3938195
cites work: Q3812929
DOI: 10.1016/J.TOPOL.2005.03.002
Recommended article: Some density results for uniformly continuous functions
Recommended article: The space of density continuous functions
Recommended article: Q5437976
Recommended article: Q3305243
Recommended article: On uniformly continuous maps between function spaces
Recommended article: Some upper bounds for density of function spaces
Recommended article: On universal Banach spaces of density continuum
Recommended article: Some density theorems in the set of continuous functions with values in the unit interval
Recommended article: Spaces of continuous functions and quasi-uniform convergence
Recommended article: Q4913387
description: scientific article; zbMATH DE number 5013523