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Approximation and the Topology of Rationally Convex Sets

Published online by Cambridge University Press:  20 November 2018

E. S. Zeron
E. S. Zeron*
Affiliation:
Depto. Matemáticas, CIVESTAV, Apdo. Postal 14-740, México DF, 07000, México, and Centre de Recherches Mathématiques, Université de Montréal, Succ. Centre-ville, CP 6128, Montréal, H3C 3J7 e-mail: eszeron@math.cinvestav.mx
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Abstract

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Considering a mapping $g$ holomorphic on a neighbourhood of a rationally convex set $K\subset {{\mathbb{C}}^{n}}$ , and range into the complex projective space $\mathbb{C}{{\mathbb{P}}^{m}}$ , the main objective of this paper is to show that we can uniformly approximate $g$ on $K$ by rational mappings defined from ${{\mathbb{C}}^{n}}$ into $\mathbb{C}{{\mathbb{P}}^{m}}$ . We only need to ask that the second Čech cohomology group ${{\overset{\scriptscriptstyle\smile}{H}}^{2}}\left( K,\mathbb{Z} \right)$ vanishes.

Keywords

32E3032Q55Rationally convexcohomology and homotopy

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 4 , 01 December 2006 , pp. 628 - 636
Copyright
Copyright © Canadian Mathematical Society 2006

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