homotopy extension property

Also compare this to the visualization of the homotopy extension property.

If has the homotopy extension property, then the simple inclusion map is a cofibration.

If is a cell complex and is a subcomplex of , then the pair has the homotopy extension property.

There is a common generalization of the homotopy lifting property and the homotopy extension property.

If the pair has this property only for a certain codomain , we say that has the homotopy extension property with respect to .

This implies that any cofibration can be treated as an inclusion map, and therefore it can be treated as having the homotopy extension property.

In mathematics, in the area of algebraic topology, the homotopy extension property indicates which homotopies defined on a subspace can be extended to a homotopy defined on a larger space.

Another useful property involving homotopy is the homotopy extension property, which characterizes the extension of a homotopy between two functions from a subset of some set to the set itself.

The homotopy extension property of is obtained by taking to be a constant map, so that is irrelevant in that every map to E is trivially the lift of a constant map to the image point of .