Given the definition of a proper metric space: a metric space is proper if every closed ball is compact. I want to show that the hyperbolic plane in the Poincare disc model is proper, but I don't know how. I tried to use Heine-Borel theorem, but I'm not sure it applies to other spaces other than the Euclidiean space. (We've only saw the disc model and the half upper plane model in class).
2026-04-03 21:00:53.1775250053
Is the Hyperbolic plane a proper space?
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