Carathéodory completeness on the plane - Edigarian, Armen (Universitatis Iagellonicae acta mathematica, 2019)
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.