Solution of a problem of P. S. Aleksandrov. (A compact space with distinct inductive dimensions)

A compact space $X$ with $\operatorname{dim}X=\operatorname{ind}X=2$, $\operatorname{Ind}X=3$ is constructed. This answers in the negative a question of P. S. Aleksandrov whether $\operatorname{ind}$ and $\operatorname{Ind}$ coincide for compact spaces.
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