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
Famous quotes containing the word definition:
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possessafter many mysterieswhat one loves.”
—François, Duc De La Rochefoucauld (16131680)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than thisdevoted and obedient. This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (18201910)
“One definition of man is an intelligence served by organs.”
—Ralph Waldo Emerson (18031882)