In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of...

bundle, so it cannot immerse in codimension 0 (in ⁠ R 2 {\displaystyle \mathbb {R} ^{2}} ⁠), though it embeds in codimension 1 (in ⁠ R 3 {\displaystyle \mathbb...

stable manifolds of the saddle. In three or more dimensions, higher codimension bifurcations can occur, producing complicated, possibly chaotic dynamics...

In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common...

between a subspace and its ambient space is known as its codimension. A hyperplane has codimension 1. In geometry, a hyperplane of an n-dimensional space...

the middle dimension has codimension more than 2: when the codimension is 2, one encounters knot theory, but when the codimension is more than 2, embedding...

or those of all prime ideals. The height is also sometimes called the codimension, rank, or altitude of a prime ideal. In a Noetherian ring, every prime...

Cross-polytope Simplex Hyperpyramid Dimensions by number Zero One Two Three Four Five Six Seven Eight n-dimensions See also Hyperspace Codimension Category...

surface). The second fundamental form can be generalized to arbitrary codimension. In that case it is a quadratic form on the tangent space with values...

something that happens in codimension two (like knot theory, and monodromy); since real codimension two is complex codimension one, the local complex example...