| Multidifferential Calculus: Chain Rule, Open Mapping and Transversal Intersection Theorems (1997) | |||||||||||||||
Abstract | |||||||||||||||
| this paper (Theorem 4.3.3). For this reason, we now believe that the more restrictive definition proposed here ought to supersede that of [15]. Since we still feel that the word used in [15] is the most adequate name for the concept, we have taken the liberty of retaining the word while slightly changing its meaning, rather than creating a new word. The proof of the open mapping theorem is an elaboration of ideas originally due to S. / Lojasiewicz Jr., and is based on a method introduced by Wazewski (cf. [21]) for the study of implicitly defined mappings. The multidifferentials at a point (¯x; ¯ y) 2 X \Theta Y of a set-valued map | |||||||||||||||
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