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 | |
Added by: | [mc] |
Total mark: | 0 |
Attachments
|
|
Notes
|
|
|
|
Topics
|
|
|