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Tameness of Complex Dimension in a Real Analytic Set

Published online by Cambridge University Press:  20 November 2018

Janusz Adamus ,
Serge Randriambololona  and
Rasul Shafikov
Janusz Adamus
Affiliation:
Department of Mathematics, The University of Western Ontario, LondonON N6A 5B7 Institute of Mathematics, Faculty of Mathematics and Computer Science, Jagiellonian University, 30-348 Kraków, Poland, e-mail: [email protected]
Serge Randriambololona
Affiliation:
Department of Mathematics, The University of Western Ontario, LondonON N6A 5B7, e-mail: [email protected]@ens-lyon.org
Rasul Shafikov
Affiliation:
Department of Mathematics, The University of Western Ontario, LondonON N6A 5B7, e-mail: [email protected]@ens-lyon.org
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Abstract

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Given a real analytic set $X$ in a complex manifold and a positive integer $d$, denote by ${{\mathcal{A}}^{d}}$ the set of points $p$ in $X$ at which there exists a germ of a complex analytic set of dimension $d$ contained in $X$. It is proved that ${{\mathcal{A}}^{d}}$ is a closed semianalytic subset of $X$.

Keywords

32B1032B2032C0732C2532V1532V4032V40complex dimensionfinite typesemianalytic settameness
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 4 , 01 August 2013 , pp. 721 - 739
Copyright
Copyright © Canadian Mathematical Society 2013

References

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