In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an ambient space, for example a manifold, taking a submanifold to another submanifold.
For example in knot theory, one considers two knots the same if one can distort one knot into the other without breaking it.
Such a distortion is an example of an ambient isotopy.
A continuous map is defined to be an ambient isotopy taking
This implies that the orientation must be preserved by ambient isotopies.
For example, two knots that are mirror images of each other are, in general, not equivalent.
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