Search results for "Definable set"

showing 2 items of 2 documents

The Kuratowski convergence and connected components

2012

International audience; We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry.

Connected componentDiscrete mathematicsSocial connectednessApplied Mathematics010102 general mathematicsDimension (graph theory)Mathematics::General Topology16. Peace & justiceKuratowski convergencesubanalytic sets01 natural sciencesKuratowski's theoremKuratowski convergence010101 applied mathematicsDefinable setMathematics::Logictame geometry0101 mathematicsLimit set[MATH]Mathematics [math]Kuratowski closure axiomsAnalysisMathematics
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On the points realizing the distance to a definable set

2011

Abstract We prove a definable/subanalytic version of a useful lemma, presumably due to John Nash, concerning the points realizing the Euclidean distance to an analytic submanifold of R n . We present a parameter version of the main result and we discuss the properties of the multifunction obtained.

Discrete mathematicsLemma (mathematics)Applied MathematicsSubanalytic setsdefinable setsSubmanifoldsubanalytic setsEuclidean distanceAlgebraMultifunctionsDefinable setDefinable setstame geometryAnalysisTame geometryMathematicsmultifunctions
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