In mathematics, especially in topology, equidimensionality is a property of a space that the local dimension is the same everywhere.
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Definition
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 Euclidean 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.
Cohen–Macaulay ring
An algebraic variety whose coordinate ring is a Cohen–Macaulay ring is equidimensional.
References
Equidimensionality Wikipedia(Text) CC BY-SA