tame topology

{{confuse|Tame manifold}}

In mathematics, a tame topology is a hypothetical topology proposed by Alexander Grothendieck in his research program Esquisse d’un programmeAlexander Grothendieck, 1984. "[http://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/EsquisseFr.pdf Esquisse d'un Programme]", (1984 manuscript), finally published in Schneps and Lochak (1997, I), pp.5-48; English transl., ibid., pp. 243-283. {{MR|1483107}} 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,{{harvnb|A'Campo|Ji|Papadopoulos|2016|loc=§ 1.}} 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.{{cite book |doi=10.1017/CBO9780511525919|title=Tame Topology and O-minimal Structures. London Mathematical Society lecture note series, no. 248|year=1998 |last1=Dries |first1=L. P. D. van den |authorlink = Lou van den Dries|isbn=9780521598385|publisher=Cambridge University Press|location=Cambridge, New York, and Oakleigh, Victoria }}{{cite web|first=Todd |last=Trimble |title=Answer to "A 'meta-mathematical principle' of MacPherson" |url=https://mathoverflow.net/q/67560 |website=MathOverflow |date=2011-06-12}} There are also some other suggestions.{{cite journal |last1=Ayala |first1=David |last2=Francis |first2=John |last3=Tanaka |first3=Hiro Lee |title=Local structures on stratified spaces |journal=Advances in Mathematics |date=5 February 2017 |volume=307 |pages=903–1028 |doi=10.1016/j.aim.2016.11.032 | doi-access=free |language=en |issn=0001-8708 |quote=We conceive this package of results as a dévissage of stratified structures in the sense of Grothendieck.|arxiv=1409.0501 }}