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. |
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| Authors | |
| Added by: | [mc] |
| Total mark: | 0 |
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