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.
Original language | English |
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Pages (from-to) | 25-33 |
Journal | Monatshefte für Mathematik |
Volume | 132 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2001 |