Equidimensionality

In mathematics, especially in topology, equidimensionality is a property of a space that the local dimension is the same everywhere.

[1] A topological space X is said to be equidimensional if for all points p in X, the dimension at p, that is dim p(X), is constant.

A scheme S is said to be equidimensional if every irreducible component has the same Krull dimension.

For example, the affine scheme Spec k[x,y,z]/(xy,xz), which intuitively looks like a line intersecting a plane, is not equidimensional.

[2][clarification needed] This topology-related article is a stub.