Ambient isotopy - Citizendia

In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an "ambient space", a manifold, taking a submanifold to another submanifold. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be In Mathematics, a submanifold of a Manifold M is a Subset S which itself has the structure of a manifold and for which the Inclusion More precisely, let N and M be manifolds and g and h be embeddings of N in M. The map f, an isotopy of the identity map of M, is defined to be an ambient isotopy taking g to h if f₁g=h. In Topology, two continuous functions from one Topological space to another are called homotopic ( Greek homos = identical

Consider a manifold M and two submanifolds A and B. An ambient isotopy can be described as a function $H_t(x) \colon M \times[0,1] \to M$ such that $H 0 (x) = id M$ and $\{H_1(a) \colon a \in A\} = B$

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