# Semi-sudden homotopy

From Topospaces

*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 be a topological space. A **semi-sudden homotopy** on is a continuous map such that:

- For any ,
- For any the map is a homeomorphism from to whatever its image is under the map