Abstract:The thesis is about the topology and geometry of metric spaces definable in an o-minimal expansion R of an ordered field (R, <, +, •). A definable metric space is a pair (X, d) consisting of a definable set X ⊆ R k and a definable (R, +, <)-valued metric. If X ⊆ R k is definable and e is the restriction of the usual euclidean metric on R k to X then (X, e) is a definable metric space, in this way the geometry of definable sets may be considered as a special case of the geometry of definable metric spaces. Exam… Show more
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