An example of a compact Hausdorff space whose Lebesgue, Brouwer, and inductive dimensions are different

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”.