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The Kuratowski convergence and connected components |
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| Authors: | Zofia Denkowska Maciej P. Denkowski |
| Affiliation: | 1. Université d?Angers, Département de Mathématiques, LAREMA, UMR CNRS no. 6093, 2, bd Lavoisier, 49 045 Angers Cédex 1, France;2. Université de Bourgogne, Institut de Mathématiques de Bourgogne, UMR CNRS no. 5584, 9, av. Alain Savary, B.P. 47870, 21 078 Dijon Cédex, France |
| Abstract: | 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. |
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