Stratified collectionsofdiffer- inamore intuitive are Expressed terminology, areas during this attribute tiable manifoldswhich are an glued jointly acceptable manner. of manifolds" characteristic turns into within the identify or unique "complexes [188] obvious of "manifold collections" See. HASSLERWHITNEY fora the by means of predecessor [189, eleven) of stratified WHITNEY's article from the 1947 smooth thought a [188] area. 12 months the beginning date of summary of stratifications. Nev- should be as an concept looked have thought of ahead of 1947 which mathematicians these days theless, already issues, of stratified like for at theend ofthe are taken care of in the concept areas, instance to while 19th whilst or century, algebraic geometers begun examine singularities and of types The curiosity in simplicialcomplexes triangulations algebraic started. of manifolds" in for the advent of the so-called used to be cause "complexes [188] bounded submanifold of the remark that the of a a few boundary noncompact decrease dimensional Euclidean oftenbe in can decomposed in the community finitelymany house inmodern manifolds. This ofviewhasbeentaken element back geometric research up and for example varieties the root of the of a or an idea manifold-with-boundary manifold-with-corners for MELROSE or RENETHOM instance [126, 127] 1.1.19). (see spotted in his paintings of 1955 that his iterated units of of asmooth singularities [1661 f R' R' manifolds for convinced services and a : -4 are common include mapping assortment" inthe ofWHITNEY WHITNEY 1957in "manifold feel proved [190] [1891.

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