Sudden contracting 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.

Definition

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

• $F(x,0)=x\mathrm{\forall }x\in X$
• 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 $F(x,1)=x_0\mathrm{\forall }x\in X$

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