# Isotopy

Let $X$ be a topological space and $f,g$ be homeomorphisms from $X$ to itself. An isotopy from $f$ to $g$ is a homotopy $F:X \times I \to X$ that starts at $f$, ends at $g$, and such that for any fixed $t$, the map $x \mapsto F(x,t)$ is a homeomorphism.