Separable determination in Banach spaces
| Type of publication: | Article |
| Citation: | |
| Publication status: | Submitted |
| Abstract: | We study a relation between three different formulations of theorems on separable determination - one using the concept of rich families, second via the concept of suitable models and third, a new one, suggested in this paper, using the notion of $\omega$-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 $\sigma$-porosity (and of similar notions) in the language of rich families; thus, not using any terminology from logic or set theory. |
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| Preprint year: | 2016 |
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| Authors | |
| Added by: | [mc] |
| Total mark: | 0 |
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