Geodesic
On~a~class of infinite-dimensional spaces
Sbornik. Mathematics, Tome 8 (1969) no. 3, pp. 409-418

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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. Bibliography: 6 titles. 
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     author = {A. I. Vainshtein},
     title = {On~a~class of infinite-dimensional spaces},
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A. I. Vainshtein. On~a~class of infinite-dimensional spaces. Sbornik. Mathematics, Tome 8 (1969) no. 3, pp. 409-418. http://geodesic.mathdoc.fr/item/SM_1969_8_3_a6/