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: The ISS is on the ground, bee.
gollark: Generally they just see some vaguely biology-related thing and news people think "OH WOW LIFE IN SPACE ÆÆÆÆÆÆÆÆÆÆÆÆ PUBLISHING IMMEDIATELY".
gollark: I am not aware of this.
gollark: Of course, it's really unlikely that there are technological civilizations around our development level around, since we don't see any at any development level.
gollark: In general. Radio telescopes are INCREASINGLY good.
References
- Wirthmüller, Klaus. A Topology Primer: Lecture Notes 2001/2002 (PDF). p. 90.
- Anand P. Sawant. Hartshorne’s Connectedness Theorem (PDF). p. 3.
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