Semi-sudden homotopy

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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

Relation with other properties

Stronger properties

• Sudden homotopy