A note on dimension theory of metric spaces

T. Przymusiński

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We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and $d i m Y = ω_{0}$ and $d i m X = ω_{0} + 1$ . Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.

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