Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topology as faithful communication through relations   Basic pairs and their morphisms are the most elementary framework in which
standard topological notions can be defined. We present here a new
interpretation of topological concepts as those which can be communicated
faithfully between the two sides of basic pairs. In particular, we prove that
the subsets which can be communicated faithfully (in the suitable way) are
exactly open subsets and closed subsets. We also prove that a relation (and in
particular a function) between two sets of points can be communicated
faithfully if and only if it is continuous.

29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
18
The categories of this paper are: econ