Abstract
We first define the topology of semi-algebraic sets and study connectedness in a general real closed field. In order to study the properties of closed and bounded semi-algebraic sets in Section 4, we introduce semi-algebraic germs in Section 3. The semi-algebraic germs over a real closed field constitute a real closed field containing infinitesimals, closely related to the field of Puiseux series, and play an important role throughout the whole book. We end the chapter with a section on semi-algebraic differentiable functions.
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Bibliographical Notes
A. Tarski, Sur les ensembles définissables de nombres réels, Fund. Math. 17, 210–239 (1931).
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© 2003 Springer-Verlag Berlin Heidelberg
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Basu, S., Pollack, R., Roy, MF. (2003). Semi-Algebraic Sets. In: Algorithms in Real Algebraic Geometry. Algorithms and Computation in Mathematics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05355-3_4
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DOI: https://doi.org/10.1007/978-3-662-05355-3_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-05357-7
Online ISBN: 978-3-662-05355-3
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