Browsing by Author "Kuuse, Karl Oskar"

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    A characterization of denting points in Banach spaces
    (Tartu Ülikool, 2024) Kuuse, Karl Oskar; Langemets, Johann, juhendaja; Perreau, Yoël, juhendaja; Tartu Ülikool. Matemaatika ja statistika instituut; Tartu Ülikool. Loodus- ja täppisteaduste valdkond
    A Banach space has the Radon–Nikod´ym Property if and only if every non-empty closed bounded convex subset of it has a denting point. The Radon–Nikod´ym property also implies the Krein–Milman Property – every closed bounded convex subset has an extreme point. It is a long-standing problem to show whether these two properties are actually different or not. The main aim of this thesis is to study denting points in various Banach spaces and prove a famous characterization of denting points as extreme points which are simultaneously points of continuity.