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RIGID SUBANALYTIC SUBSETS OF CURVES AND SURFACES

Published online by Cambridge University Press:  01 June 1999

LEONARD LIPSHITZ  and
ZACHARY ROBINSON
LEONARD LIPSHITZ
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA, [email protected]
ZACHARY ROBINSON
Affiliation:
Department of Mathematics, East Carolina University, Greenville, NC 27858, USA, [email protected]
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Abstract

Working over an algebraically closed, complete, non-Archimedean, nontrivially valued field of characteristic zero, it is shown that (i) any subanalytic subset of a one-dimensional semialgebraic set is semialgebraic, (ii) any one-dimensional subanalytic set is semianalytic, and (iii) any subanalytic subset of a two-dimensional semianalytic set is semianalytic.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 895 - 921
Copyright
The London Mathematical Society 1999

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