# Semi-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

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

• For any $x$, $F(x,0) = x$
• For any $t < 1$ the map $x \mapsto F(x,t)$ is a homeomorphism from $X$ to whatever its image is under the map