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For every natural number      n n       we construct a metrizable separable space      Y Y       such that      Y n {Y^n}       is weakly infinite-dimensional (moreover, is a      C C      -space) but      Y n + 1 {Y^{n + 1}}       is strongly infinite-dimensional.

Spaces whose 𝑛th power is weakly infinite-dimensional but whose (𝑛+1)th power is not