Cofibration

From Wikipedia, the free encyclopedia

You have new messages (last change).

In mathematics, in particular homotopy theory, a continuous mapping

i\colon A \to X,

where A and X are topological spaces, is a cofibration if it satisfies the homotopy extension property with respect to any space Y. The name is because the dual condition, the homotopy lifting property , defines fibrations.

[edit] Basic theorems

  • A cofibration is a closed inclusion (injective with closed image); for suitable spaces, a converse holds
  • Every map can be replaced by a cofibration via the mapping cylinder construction
  • There is a cofibration (A, X), if and only if there is a retraction from
X \times I
to
A \times I \cup X \times \{0\}

[edit] References

 This topology-related article is a stub. You can help Wikipedia by expanding it.
Retrieved from "http://en.wikipedia.org../../../c/o/f/Cofibration.html"