An example in dimension theory
Robert D. Anderson, James Edwin. Keisler · Proceedings of the American Mathematical Society · 1967
An example is constructed which justifies the following theorem: Theorem 2. There exists a set KEEn such that, for each positive integer, s, dim X = dim A* = dim Ku = n -1.Here dim means (inductive) topological dimension [l, p. 24], A? is the s-fold product of K with itself and K" is the denumerable product of K with itself.This result is in contrast to the known result that if A, B are nonvoid separable metric spaces with A compact and dim B>0 then dim(4 XB) =dim A, equality holding only if dim A = «>.