On a class of infinite-dimensional spaces

In the paper is given a new version of the Hurewicz–Wallman characterization of dimension. Analogously to P. S. Aleksandrov's definitions, $W$-infinite-dimensional and $S$-infinite-dimensional spaces are introduced. It is proved that $W$-infinite-dimensional spaces satisfy the heredity condition and the sum theorem. Also, mappings of infinite-dimensional spaces which increase dimension are investigated.
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