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]

  1. ^ Alexander Grothendieck, 1984. "Esquisse d'un Programme", (1984 manuscript), finally published in Schneps and Lochak (1997, I), pp.5-48; English transl., ibid., pp. 243-283. MR1483107
  2. ^ A'Campo, Ji & Papadopoulos 2016, § 1.
  3. ^ Dries, L. P. D. van den (1998). Tame Topology and O-minimal Structures. London Mathematical Society lecture note series, no. 248. Cambridge, New York, and Oakleigh, Victoria: Cambridge University Press. doi:10.1017/CBO9780511525919. ISBN 9780521598385.
  4. ^ Trimble, Todd (2011-06-12). "Answer to "A 'meta-mathematical principle' of MacPherson"". MathOverflow.
  5. ^ Ayala, David; Francis, John; Tanaka, Hiro Lee (5 February 2017). "Local structures on stratified spaces". Advances in Mathematics. 307: 903–1028. arXiv:1409.0501. doi:10.1016/j.aim.2016.11.032. ISSN 0001-8708. We conceive this package of results as a dévissage of stratified structures in the sense of Grothendieck.