Closed embeddings into pseudocompact spaces preserving the covering dimension
The main result of this note is the following theorem: Every Tikhonov space X can be \(C^*\)-embedded as a closed subset of a pseudocompact Tikhonov space Y such that dim Y\(=\dim X\). Such a result has been previously proved for the small inductive dimension and by \textit{M. V. Matveev} [Mat. Zametki 41, 377-394 (1987; Zbl 0629.54008)]. It is also shown that e.g. Vopenka's compactum X \((\dim X=1\), ind \(X=\infty)\) can not be embedded into a finite dimensional (in the sense of dim) locally pseudocompact topological group.
scientific article; zbMATH DE number 4062127