Characterization of compact spaces with noncoinciding dimensions which are subsets of products of simple spaces

摘要

In this paper we characterize closed subsets of products of simple compact spaces with noncoinciding dimensions dim and ind. In 1935 P.S. Alexandroff raized the question about the relationships between three main dimensions dim, ind, and Ind in the class of compacta and later showed that dim X ≤ ind X for any compactum X. First examples of compacta with noncoinciding dimensions dim and ind were constructed by A. Lunc and V. LokucievskiT in 1949. Then more examples of compacta with additional besides dimensional properties appeared.