Real Algebraic and Analytic Geometry

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225. Krzysztof Jan Nowak:
Decomposition into special cubes and its applications to quasi-subanalytic geometry.


Submission: 2007, December 13.

This paper deals with certain families of quasianalytic Q-functions. We present a decomposition of a relatively compact Q-semianalytic and a Q-subanalytic set into a finite union of special cubes and immersion cubes, respectively. Next, we prove Gabrielov's complement theorem for Q-subanalytic sets. Also derived are other fundamental properties of the expansion of the field $\matR$ of reals by restricted quasianalytic Q-functions.

Mathematics Subject Classification (2000): 14P15, 32B20, 26E10, 32S45, 03C64.

Keywords and Phrases: quasianalytic functions, transformation to normal crossings, special cubes, immersion cubes, quasi-subanalytic sets, quasianalytic cells.

Full text, 12p.: dvi 41k, ps.gz 127k, pdf 159k.

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