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Entropic dimension of uniform spaces. (English) Zbl 0538.54028
The concepts of entropic dimension of compact metric spaces due to Pontrjagin and Schnirelmann and the dimension of locally convex topological vector spaces due to Pietsch have been generalized to the case of a general uniform space. In the main result the author proves that for every uniform space, the generalized entropic dimension is not larger than the covering dimension. It is also shown that for certain classes of uniform spaces, the two dimensions are equal. The author concedes however that ”we do not know any example of a uniform space where the entropic dimension differs from the covering dimension”.
Reviewer: M.G.Murdeshwar
54F45 Dimension theory in general topology
54E15 Uniform structures and generalizations