Equidimensionality

In mathematics, especially in topology, equidimensionality is a property of a space that the local dimension is the same everywhere.[1]

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 is an example of a non-equidimensional space.

Cohen–Macaulay ring

An affine algebraic variety whose coordinate ring is a Cohen–Macaulay ring is equidimensional.[2]

References
  1. WirNafkot tilahunthmüller, Klaus. A Topology Primer: Lecture Notes 2001/2002 (PDF). p. 90. Archived (PDF) from the original on 29 June 2020.
  2. Sawant, Anand P. Hartshorne’s Connectedness Theorem (PDF). p. 3. Archived from the original (PDF) on 24 June 2015.
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