Three basic facts on semi-algebraic sets
Speaker: Ha Huy Vui

Time: 9h30, Tuesday, January 6, 2015

Location: Room 104, Building A5, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract:This talk describesthe proofs of the following results:

  • Cell Decomposition Theorem: Any semi-algebraic set possess a cellular decomposition, whose cells are semi-algebraic sets (a constructive proof);
  • Tarski-Seidenberg theorem: The image under a projection of a semi-algebraic set is a semi-algebraic set;
  • Whitney-Lojasiewicz theorem: Each semi-algebraic set has only finitely many (semi-algebraic)connected components.


  1.  D. Arnon, A cellular decomposition algorithm for semi-algebraic sets, Lecture Notes in Computer Science,1979.
  2.  M. Coste, An introduction to semi-algebraic geometry, 2002, (Chapter2).