Equidimensionality
In mathematics, especially in topology, equidimensionality is a property of a space that the local dimension is the same everywhere.
Definition (topology)
A topological space X is said to be equidimensional if for all points p in X, the dimension at p, that is dim p, is constant. The Euclidean space is an example of an equidimensional space. The disjoint union of two spaces X and Y of different dimension is an example of a non-equidimensional space.Definition (algebraic geometry)
A scheme S is said to be equidimensional if every irreducible component has the same Krull dimension. For example, the affine schemeSpec k/, which intuitively looks like a line intersecting a plane, is not equidimensional.