Homotopy - Homotopy Equivalence - Null-homotopy

A function f is said to be null-homotopic if it is homotopic to a constant function. (The homotopy from f to a constant function is then sometimes called a null-homotopy.) For example, a map from the circle S1 is null-homotopic precisely when it can be extended to a map of the disc D2.

It follows from these definitions that a space X is contractible if and only if the identity map from X to itself—which is always a homotopy equivalence—is null-homotopic.

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