Universal maps and surjective characterizations of completely metrizable $\textrm {LC}^ n$-spaces
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- by A. Chigogidze and V. Valov PDF
- Proc. Amer. Math. Soc. 109 (1990), 1125-1133 Request permission
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 ${\ell _2}(\tau )$.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- 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