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.
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(Received 17 August 2000)
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van Mill, J., Pol, R. Note on Weakly n-Dimensional Spaces. Mh Math 132, 25–33 (2001). https://doi.org/10.1007/s006050170056
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DOI: https://doi.org/10.1007/s006050170056