Closed embeddings into pseudocompact spaces preserving the covering dimension
type: Item
instance of: scholarly article
title: Closed embeddings into pseudocompact spaces preserving the covering dimension
zbMATH Open document ID: 0651.54006
author: S. H. Smith
published in: Moscow University Mathematics Bulletin
publication date: 1988-01-01T00:00:00Z
review text: The main result of this note is the following theorem: Every Tikhonov space X can be \(C^*\)-embedded as a closed subset of a pseudocompact Tikhonov space Y such that dim Y\(=\dim X\). Such a result has been previously proved for the small inductive dimension and by \textit{M. V. Matveev} [Mat. Zametki 41, 377-394 (1987; Zbl 0629.54008)]. It is also shown that e.g. Vopenka's compactum X \((\dim X=1\), ind \(X=\infty)\) can not be embedded into a finite dimensional (in the sense of dim) locally pseudocompact topological group.
Mathematics Subject Classification ID: 54C45
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54F45
zbMATH DE Number: 4062127
zbMATH Keywords: \(C^*\)-embedding
zbMATH Keywords: pseudocompact Tikhonov space
zbMATH Keywords: small inductive dimension
zbMATH Keywords: Vopenka's compactum
reviewed by: Ivan Ivanšić
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4062127