Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Separable determination in Banach spaces   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.
  Moreover, we prove that in Asplund spaces, generalized lushness is separably
determined.

8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph