Closure Theorem for Partially Semialgebraic Sets
Volume 55 / 2007
Bulletin Polish Acad. Sci. Math. 55 (2007), 325-331
MSC: Primary 32B20; Secondary 14P15, 32C25.
DOI: 10.4064/ba55-4-4
Abstract
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.
