Note on weakly n-dimensional spaces

Weakly n-dimensional spaces were first distinguished by Karl Menger. In thi s note we shall discuss three topics concerning this class of spaces: unive rsal spaces, products, and the sum theorem. We prove that there is a univer sal space for the class of all weakly n-dimensional spaces. present a simpl er 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 painwise disjoint countable closed cover by weakly n-dimensional s ubspaces but is not weakly n-dimensional itself.