, Volume 97, Issue 3, pp 4109-4115

Dimension axioms and decomposing mappings

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Abstract

An axiomatic definition of the covering dimension dim in the class of all (closed) subsets of finite-dimensional cubes is given relative to decomposing mappings. An axiomatic definition of the possible transfinite extension of this dimension in the class of all (closed) subsets of the Smirnov compacta is suggested. Bibliography: 15 titles.

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 20, pp. 196–207, 1997.