Definition
Let be a topological space, and let . We say that the pair has the homotopy extension property if, given a homotopy and a map such that, there exists an extension of to the homotopy such that .
That is, the pair has the homotopy extension property if any map can be extended to a map (i.e. and agree on their common domain).
If the pair has this property only for a certain codomain, we say that has the homotopy extension property with respect to .
Read more about this topic: Homotopy Extension Property
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