On spaces of group-valued functions
type: Item
instance of: scholarly article
title: On spaces of group-valued functions
zbMATH Open document ID: 1289.54066
DOI: 10.2298/FIL1102163K
author: Ljubiša D. R. Kočinac
published in: Filomat
publication date: 2013-10-18T00:00:00Z
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 54E15
Mathematics Subject Classification ID: 54H11
zbMATH DE Number: 6217182
zbMATH Keywords: selection principles
zbMATH Keywords: (strong) fan tightness
zbMATH Keywords: bornology
zbMATH Keywords: strong uniform convergence
MaRDI profile type: Publication
full work available at URL: fil1102163k
OpenAlex ID: W1986213598
Recommended article: Spaces of differentiable functions on compact groups
Recommended article: Gottlieb groups of function spaces
Recommended article: On some results in connection with topological group-valued functions
Recommended article: Group actions on spaces of rational functions
Recommended article: Space functions of groups.
Recommended article: Spaces of smooth functions and distributions on infinite-dimensional compact groups
Recommended article: Groups, special functions and rigged Hilbert spaces
Recommended article: Group structures on function spaces with the set-open topology
Recommended article: HARMONIC FUNCTION SPACES ON GROUPS
Recommended article: Q4217992
review text: The author extends several results concerning closure-type properties of continuous real-valued functions on a Tychonoff space, to the space \(C_p(X,G)\) of group-valued functions with the topology of pointwise convergence, investigated by \textit{D. Shakhmatov} and \textit{J. Spévák} [Topology Appl. 157, 1518--1540 (2010; Zbl 1195.54040)]. For example, it is proved that \(X\) satisfies the selection principle \(S_1(\Omega,\Omega)\) if and only if \(C_p(X,G)\) has countable strong fan tightness, where \(G\) is a metric group and \(X\) is a \(G^*\)-regular space.NEWLINENEWLINE In the third section, some results from the previous section and from [\textit{A. Caserta, G. Di Maio} and \textit{Lj. D. R. Kočinac}, Topology Appl. 159, 1847--1852 (2012; Zbl 1253.54021)] are extended to the function space \(C(X,G)\) endowed with the topology of strong uniform convergence on bornologies.
description: scientific article; zbMATH DE number 6217182