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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Dense embeddings of sigma-compact, nowhere locally compact metric spaces


Author: Philip L. Bowers
Journal: Proc. Amer. Math. Soc. 95 (1985), 123-130
MSC: Primary 54C25; Secondary 54D45, 54F45
MathSciNet review: 796460
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Abstract: It is proved that a connected complete separable ANR $ Z$ that satisfies the discrete $ n$-cells property admits dense embeddings of every $ n$-dimensional $ \sigma $-compact, nowhere locally compact metric space $ X(n \in N \cup \{ 0,\infty \} )$. More generally, the collection of dense embeddings forms a dense $ {G_\delta }$-subset of the collection of dense maps of $ X$ into $ Z$. In particular, the collection of dense embeddings of an arbitrary $ \sigma $-compact, nowhere locally compact metric space into Hilbert space forms such a dense $ {G_\delta }$-subset. This generalizes and extends a result of Curtis [Cu$ _{1}$].


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DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0796460-9
PII: S 0002-9939(1985)0796460-9
Keywords: Discrete $ n$-cells property, sigma-compact space, nowhere locally compact space, dense embedding, limitation topology
Article copyright: © Copyright 1985 American Mathematical Society