On J. Nagata's universal spaces
type: Item
instance of: scholarly article
title: On J. Nagata's universal spaces
zbMATH Open document ID: 0621.54025
DOI: 10.1016/0166-8641(87)90024-1
author: Elżbieta Pol
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: The author develops some interesting analogues of the classical Hurewicz- Kuratowski theorem that for a separable n-dimensional metric space X, the set of (homeomorphic) embeddings of X into \(I^{2n+1}\) is dense in the space of all continuous mappings from X into this universal space [cf. \textit{W. Hurewicz} and \textit{H. Wallman}, Dimension theory (1948; Zbl 0036.125), Theorem V3, p. 60]. J. Nagata has established universal spaces for n-dimensional or countable-dimensional spaces of weight \(\tau\) in the class of metrizable spaces (resp. strongly metrizable spaces). The author proves that in each case the set of embeddings is dense in the space of all continuous mappings into the relevant universal space of Nagata.
Mathematics Subject Classification ID: 54F45
Mathematics Subject Classification ID: 54C25
Mathematics Subject Classification ID: 54E35
Mathematics Subject Classification ID: 54C35
zbMATH DE Number: 4007231
zbMATH Keywords: zero-dimensional space
zbMATH Keywords: generalized Baire space
zbMATH Keywords: set of (homeomorphic) embeddings
zbMATH Keywords: countable-dimensional spaces
zbMATH Keywords: strongly metrizable spaces
zbMATH Keywords: universal space of Nagata
reviewed by: Bruce R. Wenner
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90024-1
OpenAlex ID: W2058305142
cites work: Einbettung metrischer Räume
cites work: Normal families and dimension theory for metric spaces
cites work: Note on dimension theory for metric spaces
cites work: On the countable sum of zero-dimensional metric spaces
cites work: On a universal n-dimensional set for metric spaces.
cites work: A remark on general imbedding theorems in dimension theory
cites work: Q5544059
cites work: Q3667577
cites work: Countable Dimensional Universal Sets
cites work: Residuality of the set of embeddings into Nagata's n-dimensional universal spaces
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description: scientific article; zbMATH DE number 4007231