nLab
contractible space

Generally

An ∞-groupoid or a topological space or another realization of the concept (∞,0)-category is contractible if it is weakly equivalent to the point.

$$(C\text{is contractible})\iff (C\stackrel{\simeq }{\to }*).$$(C \;\text{is contractible}) \Leftrightarrow (C \stackrel{\simeq}{\to} *) \,.

For topological spaces

…

see also

• locally contractible space