Topology as faithful communication through relations
Logic
2016-11-10 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1611.03078,
title = {Topology as faithful communication through relations},
author = {Samuele Maschio and Giovanni Sambin},
journal= {arXiv preprint arXiv:1611.03078},
year = {2016}
}