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Semianalytic Set


A semianalytic set X subset= R^n is a set such that, for every x in R^n, there is an open neighborhood U of x such that X intersection U is a finite Boolean combination of sets {x^_ in U:f(x^_)=0} and {x^_ in U:g(x^_)>0}, where f,g:U->R are analytic.


See also

Analytic Function, Pseudoanalytic Function, Subanalytic

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References

Marker, D. "Model Theory and Exponentiation." Not. Amer. Math. Soc. 43, 753-759, 1996.

Cite this as:

Weisstein, Eric W. "Semianalytic Set." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SemianalyticSet.html

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