Definition:Codimension

This page has been identified as a candidate for refactoring of advanced complexity. In particular: This needs to be rewritten so as to expand its scope from manifolds to the general vector space. Until this has been finished, please leave {{Refactor}} in the code. New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Refactor}} from the code.

Definition

Let $X$ be a manifold.

Let $Z$ be a submanifold of $X$.

The codimension of $Z$ in $X$ is the dimension of $X$ minus the dimension of $Z$.