In mathematics, a tame topology is a hypothetical
topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ...
proposed by
Alexander Grothendieck in his research program ''
Esquisse d’un programme
"Esquisse d'un Programme" (Sketch of a Programme) is a famous proposal for long-term mathematical research made by the German-born, French mathematician Alexander Grothendieck in 1984. He pursued the sequence of logically linked ideas in his impor ...
'' under the French name ''topologie modérée'' (moderate topology). It is a topology in which the theory of
dévissage
In algebraic geometry, dévissage is a technique introduced by Alexander Grothendieck for proving statements about coherent sheaves on noetherian schemes. Dévissage is an adaptation of a certain kind of noetherian induction. It has many applicati ...
can be applied to
stratified structures such as
semialgebraic or
semianalytic set In mathematics, particularly in the subfield of real analytic geometry, a subanalytic set is a set of points (for example in Euclidean space) defined in a way broader than for semianalytic sets (roughly speaking, those satisfying conditions requirin ...
s.
Some authors consider an
o-minimal structure In mathematical logic, and more specifically in model theory, an infinite structure (''M'',<,...) which is totally ordered by < is called an o-minimal structure if and only if every to be a candidate for realizing tame topology in the real case. Some other authors have claimed that their theory of
conically smooth stratified spaces can achieve tame topology.
See also
*
Thom's first isotopy lemma In mathematics, especially in differential topology, Thom's first isotopy lemma states: given a smooth map f : M \to N between smooth manifolds and S \subset M a closed Whitney stratified subset, if f, _S is proper and f, _A is a submersion for eac ...
References
*
External links
*https://ncatlab.org/nlab/show/tame+topology
Algebraic analysis
Geometry education
Mathematics
Stratifications
Topology
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