THe theory fo subanalytic sets is an excellent tool in various analytic-geometric contexts, including geometric control theory. One can axiomatize the notion of "behaving like the category of subanalytic sets" by introducing the notion of "analytic-geometric category". The objects of such a category share many of the hereditary and geometric finiteness properties of subanalytic sets. Proofs of the more difficult results of this nature, like the whitney-stratifiability of sets and maps in such a category, often involve the use of charts to reduce to the case of subsets of R sup n. For subsets of R sup n, the theory of o-minimal structures on the real field, an abstraction of the theory fo semialgebraic sets, provides an elelgnat and efficient setting in which to work.
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