Biholomorphic approximation of planar domains

Bryan Edmund Cain and Richard J. Tondra

Vol. 52 (1974), No. 2, 341–345

DOI: 10.2140/pjm.1974.52.341

Abstract

This paper establishes the existence of a domain (open connected subset) B of the complex plane C such that for every domain Ω ⊂ C and every compact set K ⊂ Ω, there is a biholomorphic embedding e : B → Ω, such that K ⊂ e(B) ⊂ cl [e(B)] ⊂ Ω.

Mathematical Subject Classification

Primary: 30A24

Milestones

Received: 19 July 1973

Published: 1 June 1974