Equidimensionality

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

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. The Euclidian space is an example of an equidimensional space. The disjoint union of two spaces X and Y (as topological spaces) of different dimension cedes an example of a non-equidimensional space.

An algebraic variety whose coordinate ring is Cohen–Macaulay ring is equidimensional.