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Each Copy of the Real Line in $\C^2$ is Removable

Open Access article
 Printed: Mar 2001
  • E. Santillan Zeron
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Around 1995, Professors Lupacciolu, Chirka and Stout showed that a closed subset of $\C^N$ ($N\geq 2$) is removable for holomorphic functions, if its topological dimension is less than or equal to $N-2$. Besides, they asked whether closed subsets of $\C^2$ homeomorphic to the real line (the simplest 1-dimensional sets) are removable for holomorphic functions. In this paper we propose a positive answer to that question.
Keywords: holomorphic function, removable set holomorphic function, removable set
MSC Classifications: 32D20 show english descriptions Removable singularities 32D20 - Removable singularities

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