Open Access
September 2018 Operations with slicely countably determined sets
Vladimir Kadets, Antonio Pérez, Dirk Werner
Funct. Approx. Comment. Math. 59(1): 77-98 (September 2018). DOI: 10.7169/facm/1698


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.


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Vladimir Kadets. Antonio Pérez. Dirk Werner. "Operations with slicely countably determined sets." Funct. Approx. Comment. Math. 59 (1) 77 - 98, September 2018.


Published: September 2018
First available in Project Euclid: 28 March 2018

zbMATH: 06979910
MathSciNet: MR3858280
Digital Object Identifier: 10.7169/facm/1698

Primary: 46A55 , 46B04
Secondary: 52A07

Keywords: Daugavet property , Minkowski sum , SCD set

Rights: Copyright © 2018 Adam Mickiewicz University

Vol.59 • No. 1 • September 2018
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