The Lindelöf property is \(1\)-invariant
type: Item
instance of: scholarly article
title: The Lindelöf property is \(1\)-invariant
zbMATH Open document ID: 0923.54017
DOI: 10.1016/S0166-8641(97)00219-8
published in: Topology and its Applications
publication date: 1999-10-28T00:00:00Z
review text: The main role in \(C_p\)-theory is played by the topological ring \(C_p(X)\) formed by all continuous real valued functions on a space \(X\) in the topology of pointwise convergence. A general question on \(C_p\)-theory is: when are \(C_p(X)\) and \(C_p(Y)\) linearly homeomorphic as linear topological spaces. We say that spaces \(X\) and \(Y\) are \(l\)-equivalent if \(C_p(X)\) and \(C_p(Y)\) are linearly homeomorphic. The topological properties preserved by the relation of \(l\)-equivalence are called \(l\)-invariant. In [Topological function spaces (1992; Zbl 0758.46026)] \textit{A. V. Arkhangel'skij} posed whether the Lindelöf property is \(l\)-invariant. In this paper Arkhangel'skij's question is solved.
Mathematics Subject Classification ID: 54C35
Mathematics Subject Classification ID: 54D20
Mathematics Subject Classification ID: 46E25
zbMATH DE Number: 1307923
zbMATH Keywords: topology of pointwise convergence
author: Nikolay V. Velichko
reviewed by: Shou Lin
MaRDI profile type: Publication
cites work: Q4228099
full work available at URL: s0166-8641(97)00219-8
OpenAlex ID: W1981230582
description: scientific article; zbMATH DE number 1307923