Peano-differentiable functions in O-Minimal structures
Institution: | Universität Passau |
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Department: | Informatik und Mathematik |
Degree: | PhD |
Year: | 2006 |
Record ID: | 1114673 |
Full text PDF: | https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/56 |
We discuss several aspects of Peano-differentiable functions which are definable in an o-minimal structure expanding a real closed field. After recalling some already known results about o-minimal structures we develop techniques for the intrinsic study of differentiable functions in these structures. After this we study (ordinary) differentiable functions definable in an o-minimal structure and their continuiuty properties along curves of different differentiability classes. Then we generalise (ordinary) differentiability to Peano-differentiability. We study differentiability of certain Peano-derivatives of definable functions and characterise the sets of non-continuity of these derivatives. In the end we study extendability of these functions defined on closed sets and give sufficient conditions by which we can extend functions as Peano-differentiable functions.