Note on weakly n-dimensional spaces

J. van Mill, R Pol

Research output: Contribution to JournalArticleAcademicpeer-review


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 languageEnglish
Pages (from-to)25-33
JournalMonatshefte für Mathematik
Issue number1
Publication statusPublished - 2001


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