Some applications of the topological characterizations of the sigma-compact spaces and

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

DOI:
https://doi.org/10.1090/S0002-9947-1984-0743748-7

MathSciNet review:
743748

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Abstract | References | Similar Articles | Additional Information

Abstract: We use a technique involving skeletoids in -compact metric ARs to obtain some new examples of spaces homeomorphic to the -compact linear spaces and . For example, we show that (1) every -dimensional metric linear space is homeomorphic to ; (2) every -compact metric linear space which is an AR and which contains an infinite-dimensional compact convex subset is homeomorphic to ; and (3) every weak product of a sequence of -compact metric ARs which contain Hilbert cubes is homeomorphic to .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0743748-7

Keywords:
-compact metric ARs,
skeletoids in -compact spaces,
-sets,
convex subsets of metric linear spaces,
weak products

Article copyright:
© Copyright 1984
American Mathematical Society