Real Algebraic and Analytic Geometry

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248. Stanisław Łojasiewicz, Maria-Angeles Zurro:
Closure theorem for partially semialgebraics.


Submission: 2008, January 25.

In [3] was proven 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 5.2): a semianalytic analog of Cartan-Remmert-Stein lemma with parameters.

Mathematics Subject Classification (2000): 32B20, 14P15, 32C25.

Keywords and Phrases: semianalytic sets, closure theorem.

Full text, 6p.: dvi 27k, ps.gz 135k, pdf 166k.

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