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An example of a compact Hausdorff space whose Lebesgue, Brouwer, and inductive dimensions are different
Sbornik. Mathematics, Tome 195 (2004) no. 12, pp. 1809-1822 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct an example of a separable compact Hausdorff space $B$ satisfying the first countability axiom of dimension $2=\dim B<\operatorname{Dg}B=3<\operatorname{ind}B=4=\operatorname{Ind}B$, where $\operatorname{Dg}$ is the inductive dimension invariant introduced by Brouwer in 1913 under the name “Dimensionsgrad”. 
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V. V. Fedorchuk. An example of a compact Hausdorff space whose Lebesgue, Brouwer, and inductive dimensions are different. Sbornik. Mathematics, Tome 195 (2004) no. 12, pp. 1809-1822. http://geodesic.mathdoc.fr/item/SM_2004_195_12_a6/

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