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Separable determination in Banach spaces
Type of publication: Article
Citation:
Publication status: Published
Journal: Fundamenta Mathematicae
Volume: 243
Number: 1
Year: 2018
Pages: 9-27
DOI: 10.4064/fm480-11-2017
Abstract: We study a relation between three different formulations of theorems on separable determination: one using the concept of rich families, another via the concept of suitable models, and a third, new one, suggested in this paper, using the notion of ω-monotone mappings. In particular, we show that in Banach spaces all those formulations are in a sense equivalent, and we give a positive answer to two questions of O. Kalenda and the author. Our results enable us to obtain new statements concerning separable determination of σ-porosity (and of similar notions) in the language of rich families; thus, without using any terminology from logic or set theory. Moreover, we prove that in Asplund spaces, generalized lushness is separably determined.
Keywords:
Authors Cúth, Marek
Added by: [mc]
Total mark: 0
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