A multidimensional Taylor's theorem with minimal hypothesis
J. Marshall Ash, A. Eduardo Gatto, Stephen Vági (1990)
Colloquium Mathematicae
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Displaying similar documents to “Extending o-minimal Fréchet derivatives”
A multidimensional Taylor's theorem with minimal hypothesis
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We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our...
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We define two new normability conditions on Fréchet spaces and announce some related results.
A first-order version of Pfaffian closure
Sergio Fratarcangeli (2008)
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The purpose of this paper is to extend a theorem of Speissegger [J. Reine Angew. Math. 508 (1999)], which states that the Pfaffian closure of an o-minimal expansion of the real field is o-minimal. Specifically, we display a collection of properties possessed by the real numbers that suffices for a version of the proof of this theorem to go through. The degree of flexibility revealed in this study permits the use of certain model-theoretic arguments for the first time, e.g. the compactness...