Nonseparable closed vector subspaces of separable topological vector spaces
type: Item
instance of: scholarly article
title: Nonseparable closed vector subspaces of separable topological vector spaces
zbMATH Open document ID: 1361.46001
author: Sidney A. Morris
author: Jerzy Kąkol
author: Arkady Leiderman
published in: Monatshefte für Mathematik
publication date: 2017-01-25T00:00:00Z
review text: The main results proved are the following: (1) For a separable locally convex space \(E\), the product space \(E^c\) has a nonseparable closed vector subspace if and only if \(E\) does not have the weak topology. (2) Every metrizable vector subspace of the product of any number of separable Hausdorff locally convex spaces is separable. (3) The space of all continuous real-valued functions on the classical Michael space \(M\), endowed with the topology of pointwise convergence, is separable, but contains a nonseparable closed vector subspace.
reviewed by: Zoran Kadelburg
Mathematics Subject Classification ID: 46A03
Mathematics Subject Classification ID: 54D65
zbMATH DE Number: 6677794
zbMATH Keywords: locally convex topological vector space
zbMATH Keywords: separable topological space
MaRDI profile type: Publication
full work available at URL: s00605-016-0876-2
OpenAlex ID: W2256613829
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DOI: 10.1007/S00605-016-0876-2
description: scientific article; zbMATH DE number 6677794