Zero sets of smooth functions in the Pfaffian closure of an o-minimal structure

Jones, G.

doi:10.1090/S0002-9939-08-09373-8

Zero sets of smooth functions in the Pfaffian closure of an o-minimal structure
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by G. O. Jones PDF

Proc. Amer. Math. Soc. 136 (2008), 4019-4025 Request permission

Abstract:

I show that in an o-minimal structure on the real field, satisfying certain conditions, every closed definable set is the zero set of a smooth definable function. The conditions are shown to hold in the Pfaffian closure of a polynomially bounded o-minimal structure having smooth cell decomposition.

References

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