The existence of quasiconformal homeomorphism between planes with countable marked points

Abstract

We consider quasiconformal deformations of C$\backslash$Z. We give some criteria for infinitely often punctured planes to be quasiconformally equivalent to C$\backslash$Z. In particular, we characterize the closed subsets of R whose compliments are quasiconformally equivalent to C$\backslash$Z.