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

http://dx.doi.org/10.4153/CMB-2001-016-5
Canad. Math. Bull. 44(2001), 126-128

  Published:2001-03-01
 Printed: Mar 2001

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.