Ambient isotopy
= Ambient isotopy
{title2=$F_t\in\operatorname{Homeo}(M),\quad F_0=1$}
Two embeddings $f_0,f_1:N\hookrightarrow M$ are ambient isotopic when a continuously varying family of ambient <homeomorphisms> $F_t$ starting at the identity satisfies $F_1f_0=f_1$. This is stronger than an arbitrary homotopy of maps. Smooth versions use smooth families of diffeomorphisms; unparametrized versions identify embedded images, and oriented versions preserve their orientations.