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]

gollark: It's undefined, but you know.
gollark: sqrt(x) is smaller than x so we can ignore it, and x/-x is -1.
gollark: Hmm. I would have thought it was -1.
gollark: Ugh, I am either going to have to define SO MANY types or do stuff inelegantly.
gollark: I'm not sure an array language is suited for Minoteaur™'s cool graph-based™™ design.

References
  1. Wirthmüller, Klaus. A Topology Primer: Lecture Notes 2001/2002 (PDF). p. 90.
  2. Anand P. Sawant. Hartshorne’s Connectedness Theorem (PDF). p. 3.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.