In geometric topology—for example in knot theory—the idea of isotopy is used to construct equivalence relations. For example, when should two knots be considered the same? We take two knots, "K"1 and "K"2, in three-dimensional space. A knot is an embedding of a one-dimensional space, the "loop of string" (or the circle), into this space, and this embedding gives a homeomorphism between the circle and its image in the embedding space. The intuitive idea behind the notion of knot equivalence is that one can "deform" one embedding to another through a path of embeddings: a continuous function starting at "t" = 0 giving the "K"1 embedding, ending at "t" = 1 giving the "K"2 embedding, with all intermediate values corresponding to embeddings. This corresponds to the definition of isotopy. An ambient isotopy, studied in this context, is an isotopy of the larger space, considered in light of its action on the embedded submanifold. Knots "K"1 and "K"2 are considered equivalent when there is an ambient isotopy which moves "K"1 to "K"2. This is the appropriate definition in the topological category.