An introduction to semialgebraic geometry
An introduction to semialgebraic geometry
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Jingjun Han, Princeton University
A semialgebraic set is a subset S of R^n defined by a finite听sequence of polynomial equations P=0 and inequalities Q > 0, or any听finite union of such sets. In this talk, I will introduce some basic听properties of semialgebraic sets, including that they are closed under the听projection operation and triangularizable. If time permits, I will听show an explicit bound for the number of connected components of a听real algebraic set as a function of the degree of the equations and听the dimension of the ambient space.