Some applications of the topological characterizations of the sigma-compact spaces $l^{2}_{f}$ and $\Sigma$
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- by Doug Curtis, Tadeusz Dobrowolski and Jerzy Mogilski PDF
- Trans. Amer. Math. Soc. 284 (1984), 837-846 Request permission
Abstract:
We use a technique involving skeletoids in $\sigma$-compact metric $\text {ARs}$ to obtain some new examples of spaces homeomorphic to the $\sigma$-compact linear spaces $l_f^2$ and $\Sigma$. For example, we show that (1) every ${\aleph _0}$-dimensional metric linear space is homeomorphic to $l_f^2$; (2) every $\sigma$-compact metric linear space which is an $\text {AR}$ and which contains an infinite-dimensional compact convex subset is homeomorphic to $\Sigma$; and (3) every weak product of a sequence of $\sigma$-compact metric $\text {ARs}$ which contain Hilbert cubes is homeomorphic to $\Sigma$.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 284 (1984), 837-846
- MSC: Primary 54F65; Secondary 54B10, 54C25, 54D45, 57N20
- DOI: https://doi.org/10.1090/S0002-9947-1984-0743748-7
- MathSciNet review: 743748