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 algebraic variety whose coordinate ring is a Cohen–Macaulay ring is equidimensional.[2]
References
- ^ Wirthmüller, Klaus. A Topology Primer: Lecture Notes 2001/2002 (PDF). p. 90.
- ^ Anand P. Sawant. Hartshorne’s Connectedness Theorem (PDF). p. 3.
