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A counting theorem on semi-algebraic set and its applications. (Chinese. English summary) Zbl 0955.14041

Summary: In this paper, a counting theorem about the cardinality of semi-algebraic set is given by using Tarski’s principle. Basing on the principle, a method to calculate the Euler characteristic and the genus of a compact algebraic manifold is presented.

MSC:

14P10 Semialgebraic sets and related spaces
03E10 Ordinal and cardinal numbers
13J30 Real algebra
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