Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Net convergence structures with applications to vector lattices   Convergence is a fundamental topic in analysis that is most commonly modelled
using topology. However, there are many natural convergences that are not given
by any topology; e.g., convergence almost everywhere of a sequence of
measurable functions and order convergence of nets in vector lattices. The
theory of convergence structures provides a framework for studying more general
modes of convergence. It also has one particularly striking feature: it is
formalized using the language of filters. This paper develops a general theory
of convergence in terms of nets. We show that it is equivalent to the
filter-based theory and present some translations between the two areas. In
particular, we provide a characterization of pretopological convergence
structures in terms of nets. We also use our results to unify certain topics in
vector lattices with general convergence theory.

11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci