In Singularity Theory
In singularity theory, there is a different meaning, of a decomposition of a topological space X into disjoint subsets each of which is a topological manifold (so that in particular a stratification defines a partition of the topological space). This is not a useful notion when unrestricted; but when the various strata are defined by some recognisable set of conditions (for example being locally closed), and fit together manageably, this idea is often applied in geometry. Hassler Whitney and René Thom first defined formal conditions for stratification. See topologically stratified space.
Read more about this topic: Stratification (mathematics)
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