isotopy

Let $M$ and $N$ be manifolds and $I=[0,1]$ the closed unit interval. A smooth map $h:M\times I\to N$ is called an isotopy if the restriction map $h_t:=h(-,t):M\to N$ is an embedding for all $t\in I$.

In particular, a diffeotopy is an isotopy.

Remark. Given an isotopy $h:M\times I\to N$, there exists a diffeotopy $g:N\times I\to N$ such that $h_t=g_t\circ h_0$.