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In mathematics, especially in topology, a stratified space is a topological space that admits or is equipped with a stratification, a decomposition into subspaces, which are nice in some sense (e.g., smooth or flat[1]).
A basic example is a subset of a smooth manifold that admits a Whitney stratification. But there is also an abstract stratified space such as a Thom–Mather stratified space.
On a stratified space, a constructible sheaf can be defined as a sheaf that is locally constant on each stratum.
Among the several ideals, Grothendieck's Esquisse d’un programme considers (or proposes) a stratified space with what he calls the tame topology.
In mathematics, especially in topology, a stratifiedspace is a topological space that admits or is equipped with a stratification, a decomposition into...
Thom–Mather stratifiedspace, and proved that every Whitney stratification is a Thom–Mather stratifiedspace and hence is a topologically stratifiedspace. Another...
locally compact space, and one uses Euler characteristics with compact supports, no assumptions on M or N are needed. if X is a stratifiedspace all of whose...
une variété différentielle (a differential variety). Stratifiedspace A "stratifiedspace" is a space that can be divided into pieces ("strata"), with each...
normal stratified squamous epithelium and the metaplasic epithelium of Barrett's esophagus (left of image). Alcian blue stain. Non-keratinized stratified squamous...
corrected for disproportionate sampling costs using stratified sample sizes. The reasons to use stratified sampling rather than simple random sampling include...
In mathematics, stratified Morse theory is an analogue to Morse theory for general stratifiedspaces, originally developed by Mark Goresky and Robert MacPherson...
as stratified (layered), or compound, either squamous, columnar or cuboidal. In some tissues, a layer of columnar cells may appear to be stratified due...
in X, a compact ( n − i − 1 ) {\displaystyle (n-i-1)} -dimensional stratifiedspace L, and a filtration-preserving homeomorphism U ≅ R i × C L {\displaystyle...
process, randomly and entirely by chance. Stratified randomization is considered a subdivision of stratified sampling, and should be adopted when shared...
Matthias Kreck. The basic idea is similar to that of a topologically stratifiedspace, but adapted to differential topology. Before we come to stratifolds...
associated to topological spaces, which may be a real or complex manifold, or more general topologically stratifiedspaces, possibly singular. The concept...
applies is that of a constructible sheaf. Let X be a topologically stratifiedspace. In particular, X comes with a sequence of closed subsets X = X n ⊃...
constant sheaf on U. It is also called a local system. When X is a stratifiedspace, a constructible sheaf is roughly a sheaf that is locally constant...
morphisms. A normal complex variety X has the property, when viewed as a stratifiedspace using the classical topology, that every link is connected. Equivalently...
^{-1}(0)/G} is a stratified symplectic space, i.e. a stratifiedspace with compatible symplectic structures on the strata. The space Ω 1 ( Σ , g ) {\displaystyle...
ISBN 3-88538-006-4. Pflaum, Markus J. (2001). Analytic and geometric study of stratifiedspaces. Lecture Notes in Mathematics. Vol. 1768. Berlin: Springer. ISBN 3-540-42626-4...
purposes, reverse the conventions for indexing the stratifications in a stratifiedspace, and index the open strata not by their dimension, but by their co-dimension...
Francis, John; Tanaka, Hiro Lee (5 February 2017). "Local structures on stratifiedspaces". Advances in Mathematics. 307: 903–1028. arXiv:1409.0501. doi:10...
many names: Stratified hot water storage tank with closed water circuit, stratified thermal storage, thermocline tank and water stratified tank storage...
1960s showed that these conditions give a very robust definition of stratifiedspace. The singularities in low dimension of smooth mappings, later to come...
the inaccessibility of resources and lack of social mobility found in stratified societies. Many sociological theorists have criticized the fact that the...
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