Sudden homotopy

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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.