Editing Homotopy (section)

===Properties===

Continuous functions ''f'' and ''g'' are said to be homotopic if and only if there is a homotopy ''H'' taking ''f'' to ''g'' as described above. Being homotopic is an [[equivalence relation]] on the set of all continuous functions from ''X'' to ''Y''. 
This homotopy relation is compatible with [[function composition]] in the following sense: if {{nowrap|1=''f''<sub>1</sub>, ''g''<sub>1</sub> : ''X'' → ''Y''}} are homotopic, and {{nowrap|1=''f''<sub>2</sub>, ''g''<sub>2</sub> : ''Y'' → ''Z''}} are homotopic, then their compositions {{nowrap|1=''f''<sub>2</sub>&thinsp;∘&thinsp;''f''<sub>1</sub>}} and {{nowrap|1=''g''<sub>2</sub>&thinsp;∘&thinsp;''g''<sub>1</sub> : ''X'' → ''Z''}} are also homotopic.