Sudden contracting 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

Let X be a topological space. A sudden contracting homotopy on X is a map F: X \times I \to X such that:

  • F(x,0) = x \ \forall \ x \in X
  • For any t < 1, the map sending x to F(x,t) is a homeomorphism
  • There exists a point x_0 \in X such that F(x,1) = x_0 \ \forall \ x \in X

A topological space which has a sudden contracting homotopy is termed a suddenly contractible space.