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 cedes 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.

Dimension

Dimensional spaces	Vector space Euclidean space Affine space Projective space Free module Manifold Algebraic variety Spacetime

Other dimensions	Krull Homological Lebesgue covering Inductive Hausdorff Minkowski Fractal Degrees of freedom

Polytopes and shapes	Hyperplane Hypersurface Hypercube Hypersphere Hyperrectangle Demihypercube Cross-polytope Simplex

Dimensions by number	Zero One Two Three Four Five Six (degrees of freedom) Seven Eight Nine Ten n-dimensions Negative dimensions

Category

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