TY - JOUR
TI - Carathéodory completeness on the plane
AU - Edigarian, Armen
TI - Carathéodory completeness on the plane
AB - 
	M. A. Selby [8-10] and, independently, N. Sibony [11] proved that on the complex plane c-completeness is equivalent to c-finitely compactness. Their proofs are quite similar and are based on [4]. We give more refined equivalent conditions and, along the way, simplify the proofs.

	2010 Mathematics Subject Classification. 30H05, 30H50.

	
		The author was supported in part by the Polish National Science Centre (NCN) grant no. 2015/17/B/ST1/00996.

VL - 2019
IS - Tom 56
PY - 2019
SN - 0083-4386
C1 - 2084-3828
SP - 15
EP - 21
DO - 10.4467/20843828AM.19.002.12110
UR - https://ejournals.eu/czasopismo/universitatis-iagellonicae-acta-mathematica/artykul/caratheodory-completeness-on-the-plane
KW - Carathéodory  distance
KW - completeness
KW - Melnikov's theorem
KW - peak function