Caratheodory completeness on the complex plane
Armen Edigarian
TL;DR
This paper explores Caratheodory completeness on the complex plane, providing a local version of existing equivalence results and simplifying the proofs involved.
Contribution
It introduces a local perspective on Caratheodory completeness and offers simplified proofs of known equivalences in the complex plane.
Findings
Established a local version of Caratheodory completeness results
Simplified the proofs of existing theorems
Confirmed the equivalence between Caratheodory completeness and finite compactness
Abstract
In 1975 N. Sibony and, independently, M. A. Selby proved that on the complex plane -completeness is equivalent to -finitely compactness. In the paper we give a local version of their results. We also simplify the proofs.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · advanced mathematical theories