Editing Homotopy (section)

===Null-homotopy===
A function <math>f</math> is said to be '''null-homotopic''' {{anchor|null homotopic}} if it is homotopic to a constant function.  (The homotopy from <math>f</math> to a constant function is then sometimes called a '''null-homotopy'''.)  For example, a map <math>f</math> from the [[unit circle]] <math>S^1</math> to any space <math>X</math> is null-homotopic precisely when it can be continuously extended to a map from the [[unit disk]] <math>D^2</math> to <math>X</math> that agrees with <math>f</math> on the boundary.

It follows from these definitions that a space <math>X</math> is contractible if and only if the identity map from <math>X</math> to itself&mdash;which is always a homotopy equivalence&mdash;is null-homotopic.