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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Universal maps and surjective characterizations of completely metrizable $ {\rm LC}\sp n$-spaces


Authors: A. Chigogidze and V. Valov
Journal: Proc. Amer. Math. Soc. 109 (1990), 1125-1133
MSC: Primary 54E55; Secondary 54C55
DOI: https://doi.org/10.1090/S0002-9939-1990-1009987-3
MathSciNet review: 1009987
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Abstract: We construct an $ n$-dimensional completely metrizable $ AE(n)$-space $ P(n,\tau )$ of weight $ \tau \geq \omega $ with the following property: for any at most $ n$-dimensional completely metrizable space $ Y$ of weight $ \leq \tau $ the set of closed embeddings $ Y \to P\left( {n,\tau } \right)$ is dense in the space $ C\left( {Y,P\left( {n,\tau } \right)} \right)$. It is also shown that completely metrizable $ L{C^n}$-spaces of weight $ \tau \geq \omega $ are precisely the $ n$-invertible images of the Hilbert space $ {\ell _2}(\tau )$.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1009987-3
Keywords: Strongly $ (n,\tau )$-universal map, $ n$-soft map, $ AE(n,m)$-space
Article copyright: © Copyright 1990 American Mathematical Society