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 ho ...
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 applica ...
can be applied to
stratified structures such as
semialgebraic or
semianalytic sets.
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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