Real Algebraic and Analytic Geometry |

Closure theorem for partially semialgebraics.

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Submission: 2008, January 25.

*Abstract:
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.

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