Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Some applications of the topological characterizations of the sigma-compact spaces $ l\sp{2}\sb{f}$ and $ \Sigma $

Authors: Doug Curtis, Tadeusz Dobrowolski and Jerzy Mogilski
Journal: Trans. Amer. Math. Soc. 284 (1984), 837-846
MSC: Primary 54F65; Secondary 54B10, 54C25, 54D45, 57N20
MathSciNet review: 743748
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Abstract: We use a technique involving skeletoids in $ \sigma $-compact metric 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 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 ARs which contain Hilbert cubes is homeomorphic to $ \Sigma $.

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Keywords: $ \sigma $-compact metric ARs, skeletoids in $ \sigma $-compact spaces, $ Z$-sets, convex subsets of metric linear spaces, weak products
Article copyright: © Copyright 1984 American Mathematical Society