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Closure Theorem for Partially Semialgebraic Sets

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Zurro M.-A.

Bulletin of the Polish Academy of Sciences. Mathematics

2007

tom 55

nr 4

325-331

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.

Summability "au plus petit terme"

100%

Zurro M.-A.

Studia Mathematica

1995

tom 113

nr 2

197-198

There is a curious phenomenon in the theory of Gevrey asymptotic expansions. In general the asymptotic formal power series is divergent, but there is some partial sum which approaches the value of the function very well. In this note we prove that there exists a truncation of the series which comes near the function in an exponentially flat way.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Studia Mathematica

2 Zurro M.-A.

1 2007

1 1995

Wyniki wyszukiwania

Closure Theorem for Partially Semialgebraic Sets

Summability "au plus petit terme"