Hyperbolicity and Vitali properties of unbounded domains in Banach spaces
Tom 119 / 2017
Annales Polonici Mathematici 119 (2017), 255-273 MSC: Primary 32F45, 32Q45; Secondary 32H02, 32A07, 32K05. DOI: 10.4064/ap4146-8-2017 Opublikowany online: 26 September 2017
Let $\varOmega $ be an unbounded domain in a Banach space. In this work, we wish to impose local conditions on the boundary points of $\varOmega $ (including the point at infinity) that guarantee hyperbolicity and complete hyperbolicity of $\varOmega .$ We also search for local boundary conditions so that Vitali properties hold true for $\varOmega .$ These properties might be considered as analogues of the usual taut property in the finite-dimensional case.