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The t-invariant of analytic set germs of dimension 2

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2001
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Elsevier Science B.V. (North-Holland)
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Let X-0 subset of R-n be an analytic set germ of dimension 2. We study the invariant t(X-0) defined as the least integer t such that any open semianalytic set germ of Xo can be written as a union of t basic open set germs. It is known that 2 less than or equal to t(X-0) less than or equal to 3. In this note we provide a geometric criterion to determine the exact value of t(X-0).
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C. Andradas, L. BrKocker, J. Ruiz, Constructible Sets in Real Geometry, Ergeb. der Math., Vol. 33, Berlin,Springer, 1996, p. 3 folge. C. Andradas, J. Ruiz, Algebraic and Analytic Geometry of Fans, Memoirs AMS 553 American Mathematical Society, Providence, RI, 1995. J. Bochnak, M. Coste, M.F. Roy, G)eom)etrie Alg)ebrique R)eelle, Springer, Berlin, 1987. A. Díaz-Cano, Ph.D. Thesis, U.C.M., Madrid, 1999. A. Díaz-Cano, C. Andradas, Stability index of closed semianalytic set germs, Math. Zeit. 229 (1998)743–751. R. Narasimhan, Introduction to the Theory of Analytic Spaces, Springer, Berlin, 1966. J. Ruiz, A note on a separation problem, Arch. Math. 43 (1984) 422–426. [8] J. Ruiz, The Basic Theory of Power Series, Advanced Lectures in Mathematics, Vieweg, Braunschweig,1993.
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