6533b82efe1ef96bd129298e
RESEARCH PRODUCT
The Kuratowski convergence and connected components
Zofia DenkowskaMaciej P. Denkowskisubject
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 axiomsAnalysisMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-03-01 |