# Sudden homotopy

From Topospaces

*This term is nonstandard and is being used locally within the wiki. For its use outside the wiki, please define the term when using it.*

*This article defines a property of a homotopy from a topological space to itself*

## Definition

A **sudden homotopy** on a topological space is a continuous map such that and for any the map is a homeomorphism from to .

Of particular interest is sudden contracting homotopy which is both sudden and contracting.