On the Number of Connected Components of the Relative Closure of a Semi-Pfaffian Family

The notion of relative closure (X, Y )0 of a semi-Pfaffian couple (X, Y ) was introduced by Gabrielov to give a description of the o-minimal structure generated by Pfaffian functions. In this paper, an effective bound is given for the number of connected components of (X, Y )0 in terms of the Pfaffian complexity of X and Y.

• Type: Conference
• Year: 2001
• Where: DIMACS
• Authors: Andrei Gabrielov, Thierry Zell
• Keywords: DIMACS 2001, Effective Bound, Relative Closure, Semi-Pfaffian Couple, Theoretical Computer Science