@phdthesis{Fischer2005, author = {Fischer, Andreas}, title = {Peano-differentiable functions in O-Minimal structures}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:739-opus-673}, school = {Universit{\"a}t Passau}, year = {2005}, abstract = {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.}, subject = {Semialgebraische Menge}, language = {en} }