Lebesgue covering dimension

Summary

The Lebesgue covering dimension of a topological space is the least $n$ with the following property. Every finite open cover can be refined to an open cover in which no point lies in more than $n + 1$ sets. It is a topological invariant, and it gives $n$ for the Euclidean space $\R^n$. It is one of the main notions of dimension theory, together with the inductive dimensions.