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Closure Theorem for Partially Semialgebraic Sets

María-Angeles Zurro (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

In 1988 it was proved by the first author that the closure of a partially semialgebraic set is partially semialgebraic. The essential tool used in that proof was the regular separation property. Here we give another proof without using this tool, based on the semianalytic L-cone theorem (Theorem 2), a semianalytic analog of the Cartan-Remmert-Stein lemma with parameters.

Codimension one foliations on complex tori

Marco Brunella (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.

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