Operations with slicely countably determined sets
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The notion of slicely countably determined (SCD) sets was introduced in 2010 by A.~Avilés, V.~Kadets, M.~Martín, J.~Merí and V.~Shepelska. We solve in the negative some natural questions about preserving being SCD by the operations of union, intersection and Minkowski sum. Moreover, we demonstrate that corresponding examples exist in every space with the Daugavet property and can be selected to be unit balls of some equivalent norms. We also demonstrate that almost SCD sets need not be SCD, thus answering a question posed by A. Avilés et al.
Daugavet property, Convex sets in topological linear spaces; Choquet theory, 46B04, 52A07, Functional Analysis (math.FA), Mathematics - Functional Analysis, 46A55, 52A07, slicely countably determined set, SCD set, FOS: Mathematics, Isometric theory of Banach spaces, Minkowski sum, Convex sets in topological vector spaces (aspects of convex geometry), 46B04
Daugavet property, Convex sets in topological linear spaces; Choquet theory, 46B04, 52A07, Functional Analysis (math.FA), Mathematics - Functional Analysis, 46A55, 52A07, slicely countably determined set, SCD set, FOS: Mathematics, Isometric theory of Banach spaces, Minkowski sum, Convex sets in topological vector spaces (aspects of convex geometry), 46B04
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