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On Prime Ends and Plane Continua
Author(s) -
Carmona J. J.,
Pommerenke C.
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003587
Subject(s) - bijection , prime (order theory) , conformal map , section (typography) , boundary (topology) , order (exchange) , metric (unit) , mathematics , plane (geometry) , unit (ring theory) , unit disk , combinatorics , set (abstract data type) , pure mathematics , geometry , domain (mathematical analysis) , physics , mathematical analysis , computer science , engineering , operations management , mathematics education , finance , economics , operating system , programming language
Let f be a conformal map of the unit disk D onto the domain G ⊂ Ĉ = C ∪{∞}. We shall always use the spherical metric in Ĉ . Carathéodory [ 3 ] introduced the concept of a prime end of G in order to describe the boundary behaviour of f in geometric terms; see for example [ 6 , Chapter 9] or [ 12 , Section 2.4]. There is a bijective map f ^ of T = ∂ D onto the set of prime ends of G .