In the talk I will introduce analogues of the classical notions of the complex analysis to the setting of generalised convexity and I will demonstrate that the Cartan-Thullen theorem and its appropriate formulation in the context of generalised convexity, which I will present, can be regarded as consequences of the classical theorems of functional analysis: the Banach-Steinhaus theorem and the Banach-Alaoglu theorem. Furthermore, I will provide a characterisation of the domains of holomorphy, and their generalisations, as the spaces that are complete, or as the spaces exhaustible by suitably defined polytopes. I will also provide an abstract analogue of the Levi problem and its elementary resolution.

Meeting Id: 974 3865 7180 Password: 268545