Sudden homotopy

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 $X$ is a continuous map $F:X\times I\to X$ such that $F(x,0)=x\ \forall \ x$ and for any $t<1$ the map $x\mapsto F(x,t)$ is a homeomorphism from $X$ to $X$.

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