Sipacheva O. There are no product and subgroup theorems for the covering dimension of topological groups // arXiv:2507.14889 [math.GN]. — 2025.
Аннотация
Strongly zero-dimensional topological groups G1, G2, and G such that G1×G2 has positive covering dimension and G contains a closed subgroup of positive covering dimension are constructed. Moreover, all finite powers of G1 are Lindelöf and G2 is second-countable. An example of a strongly zero-dimensional space X whose free, free Abelian, and free Boolean topological groups have positive covering dimension is also given.