Tame topology

Not to be confused with Tame manifold.

In mathematics, a tame topology is a hypothetical topology proposed by Alexander Grothendieck in his research program Esquisse d’un programme^[1] under the French name topologie modérée (moderate topology). It is a topology in which the theory of dévissage can be applied to stratified structures such as semialgebraic or semianalytic sets,^[2] and which excludes some pathological spaces that do not correspond to intuitive notions of spaces.

Some authors consider an o-minimal structure to be a candidate for realizing tame topology in the real case.^[3][4] There are also some other suggestions.^[5]

See also

• Thom's first isotopy lemma