Geodesic
Closure Theorem for Partially Semialgebraic Sets
Stanis/law /Lojasiewicz   ; María-Angeles Zurro 1
1 Departamento de Matemáticas Universidad Autónoma de Madrid 28049 Madrid, Spain
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 4, pp. 325-331 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/ba55-4-4
Keywords: proved first author closure partially semialgebraic set partially semialgebraic essential tool proof regular separation property here another proof without using tool based semianalytic l cone theorem theorem semianalytic analog cartan remmert stein lemma parameters

Stanis/law /Lojasiewicz    ; María-Angeles Zurro  1

1 Departamento de Matemáticas Universidad Autónoma de Madrid 28049 Madrid, Spain 
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Stanis/law /Lojasiewicz; María-Angeles Zurro. Closure Theorem for Partially Semialgebraic Sets. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 55 (2007) no. 4, pp. 325-331. doi: 10.4064/ba55-4-4

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