In mathematics, a tame topology is a hypothetical
topology
Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...
proposed by
Alexander Grothendieck
Alexander Grothendieck, later Alexandre Grothendieck in French (; ; ; 28 March 1928 – 13 November 2014), was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry. His research ext ...
in his research program ''
Esquisse d’un programme'' 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 applicat ...
can be applied to
stratified structures such as
semialgebraic or
semianalytic sets, and which excludes some
pathological
Pathology is the study of disease. The word ''pathology'' also refers to the study of disease in general, incorporating a wide range of biology research fields and medical practices. However, when used in the context of modern medical treatme ...
spaces that do not correspond to intuitive notions of spaces.
Some authors consider an
o-minimal structure In mathematical logic, and more specifically in model theory, an infinite structure (''M'',<,...) that 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
Real may refer to:
Currencies
* Argentine real
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* Spanish real
* Spanish colonial real
Nature and science
* Reality, the state of things as they exist, rathe ...
case. There are also some other suggestions.
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 ea ...
References
*
External links
*https://ncatlab.org/nlab/show/tame+topology
Algebraic analysis
Stratifications
Topology
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