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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2012

The Kuratowski convergence and connected components

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Résumé

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.

Dates et versions

hal-03031585 , version 1 (30-11-2020)

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Sophia Denkowska, Maciej Denkowski. The Kuratowski convergence and connected components. Journal of Mathematical Analysis and Applications, 2012, 387 (1), pp.48 - 65. ⟨10.1016/j.jmaa.2011.08.058⟩. ⟨hal-03031585⟩
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