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.