Dense embeddings of nowhere locally compact separable metric spaces
type: Item
instance of: scholarly article
title: Dense embeddings of nowhere locally compact separable metric spaces
zbMATH Open document ID: 0624.54014
DOI: 10.1016/0166-8641(87)90021-6
author: Philip L. Bowers
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: Let all spaces be separable metric. \textit{D. W. Curtis} [ibid. 16, 253-257 (1983; Zbl 0516.54013)] proved that every \(\sigma\)-compact space can be densely imbedded in Hilbert space. In this important paper, via a very interesting technique, the author extends this result. He proes that X is nowhere locally compact if and only if X imbeds densely in Hilbert space; as a consequence, every nowhere locally compact space can be densely imbedded in the Hilbert cube. In addition, X is nowhere locally compact and of dimension at most n if and only if X imbeds densely in the n- dimensional Menger-Nöbeling space; as a consequence, every nowhere locally compact space that is at most n-dimensional embeds densely in the n-dimensional Menger space.
reviewed by: Jan van Mill
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54E45
Mathematics Subject Classification ID: 54F45
zbMATH DE Number: 4013508
zbMATH Keywords: dense embedding
zbMATH Keywords: discrete n-cells property
zbMATH Keywords: limitation topology
zbMATH Keywords: nowhere locally compact space
zbMATH Keywords: Hilbert cube
zbMATH Keywords: n-dimensional Menger-Nöbeling space
zbMATH Keywords: n-dimensional Menger space
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90021-6
OpenAlex ID: W1998185844
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description: scientific article; zbMATH DE number 4013508