Inductive dimension

Summary

The inductive dimensions of a topological space are defined by induction from the dimension of boundaries. A space has dimension at most $n$ when points, or closed sets, have small neighbourhoods whose boundaries have dimension at most $n - 1$. There are two versions, the small inductive dimension $\operatorname{ind}$ and the large inductive dimension $\operatorname{Ind}$. For separable metric spaces both agree with the Lebesgue covering dimension.