Real Algebraic and Analytic Geometry
Submission: 2008, January 25.
In  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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