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Arc-properties of functions definable in o-minimal structures

Thursday 7th April 2005 - 10:00 to 10:30
INI Seminar Room 1

There are two topics at the base of this talk: arc-analytic functions (mostly studied in the subanalytic setting) and the relationships between o-minimal structures and Hardy fields. They lead us to study the following problem: for a function definable in some o-minimal structure (over the field of reals), what kind of property may be detected in restriction to some "small" space of definable arcs. We shall prove for instance that for most classical polynomially bounded o-minimal structures, continuity is equivalent to continuity on restriction to polynomial arcs. We will finish with problems of arc-definability for which we will give several open questions.

Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons