A homotopy from one embedding of a manifold 
in 
to another such that at every time, it is an embedding. The
notion of isotopy is category independent, so notions of topological, piecewise-linear,
smooth, isotopy (and so on) exist. When no explicit mention is made, "isotopy"
usually means "smooth isotopy."
Isotopy
See also
Ambient Isotopy, Regular IsotopyExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Isotopy." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Isotopy.html