Geodesic
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

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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”. 
@article{SM_2004_195_12_a6,
     author = {V. V. Fedorchuk},
     title = {An example of a~compact {Hausdorff} space whose {Lebesgue,} {Brouwer,} and inductive dimensions are different},
     journal = {Sbornik. Mathematics},
     pages = {1809--1822},
     publisher = {mathdoc},
     volume = {195},
     number = {12},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2004_195_12_a6/}
}
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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/