Stereotype locally convex spaces
type: Item
instance of: scholarly article
title: Stereotype locally convex spaces
zbMATH Open document ID: 0996.46001
author: Sergei S. Akbarov
published in: Izvestiya: Mathematics
publication date: 2002-10-31T00:00:00Z
Mathematics Subject Classification ID: 46A03
Mathematics Subject Classification ID: 46A20
zbMATH DE Number: 1592062
zbMATH Keywords: stereotype locally concise spaces
zbMATH Keywords: pseudocomplete
zbMATH Keywords: pseudosaturated
zbMATH Keywords: totally bounded Cauchy net
MaRDI profile type: Publication
DOI: 10.1070/IM2000V064N04ABEH000294
review text: The author gives complete proofs of some results on stereotype locally concise spaces which where announced in [\textit{S. S. Akbarov}, Mat. Zametki 57, No. 3, 463-466 (1995); Engl. transl. Math. Notes 57, No. 3, 319-322 (1995; Zbl 0836.46002)].NEWLINENEWLINENEWLINEA LCS space \(X\) (locally convex space) is called stereotype if it is pseudocomplete and pseudosaturated, this is:NEWLINENEWLINENEWLINE(i) every totally bounded Cauchy net converges in \(X\);NEWLINENEWLINENEWLINE(ii) every closed balanced set \(D\subset X\) with the property that for every totally bounded subset \(S\subset X\) there is a neighbourhood \(U\) of zero in \(\mathbb{X}\) such that \(S\cap U\subseteq M\), is itself a neighborhood of zero.
reviewed by: Ioana Ciorănescu
description: scientific article