TY  - JOUR
T1  - Separable determination in Banach spaces
A1  - Cúth, Marek
JA  - Fundamenta Mathematicae
Y1  - 2018
VL  - 243
IS  - 1
SP  - 9
EP  - 27
M2  - doi: 10.4064/fm480-11-2017
N2  - 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.
ER  -