在平面上的carathimodory完备性

IF 4.9 1区数学 Q1 MATHEMATICS Acta Mathematica Pub Date : 2020-01-01 DOI:10.4467/20843828am.19.002.12110

A. Edigarian

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引用次数: 1

摘要

． M. A. Selby[8-10]和N. Sibony[11]分别证明了在复平面上c -完备性等价于c -有限紧性。它们的证明非常相似，都基于[4]。我们给出了更精细的等价条件，同时简化了证明。

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Carathéodory completeness on the plane

. M. A. Selby [ 8–10 ] and, independently, N. Sibony [ 11 ] proved that on the complex plane c -completeness is equivalent to c -ﬁnitely com-pactness. Their proofs are quite similar and are based on [ 4 ]. We give more reﬁned equivalent conditions and, along the way, simplify the proofs.

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