Note on Weakly n-Dimensional Spaces |
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Authors: | Jan van Mill Roman Pol |
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Institution: | (1) Vrije Universiteit, Amsterdam, The Netherlands, NL;(2) University of Warsaw, Poland, PL |
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Abstract: | Weakly n-dimensional spaces were first distinguished by Karl Menger. In this note we shall discuss three topics concerning this class
of spaces: universal spaces, products, and the sum theorem. We prove that there is a universal space for the class of all
weakly n-dimensional spaces, present a simpler proof of Tomaszewski’s result about the dimension of a product of weakly n-dimensional spaces, and show that there is an n-dimensional space which admits a pairwise disjoint countable closed cover by weakly n-dimensional subspaces but is not weakly n-dimensional itself.
(Received 17 August 2000) |
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Keywords: | 2000 Mathematics Subject Classification: 54F45 |
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