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Each Copy of the Real Line in is Removable

Published online by Cambridge University Press:  20 November 2018

E. Santillan Zeron*
Department of Mathematics University of Toronto Toronto, Ontario M5S 3G3, email:
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Around 1995, Professors Lupacciolu, Chirka and Stout showed that a closed subset of ${{\mathbb{C}}^{N}}\left( N\ge 2 \right)$ is removable for holomorphic functions, if its topological dimension is less than or equal to $N\,-\,2$. Besides, they asked whether closed subsets of ${{\mathbb{C}}^{2}}$ 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.

Research Article
Copyright © Canadian Mathematical Society 2001


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