Topology as Faithful Communication Through Relations

Article type: Research Article

Authors: Maschio, Samuele | Sambin, Giovanni^{; *}

Affiliations: Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Via Trieste 63, 35131 Padova, Italy. maschiomath.unipd.it, [email protected]

Correspondence: [*] Address for correspondence: Dipartimento di Matematica “Tullio Levi-Civita”, Università di Padova, Padova, Italy.

Abstract: We present here a new interpretation of topological concepts based on communication. The context that allows us to see this is that of basic pairs, the most elementary structures that allow to present topology. In particular, we prove that the subsets which can be communicated faithfully between the sides of a basic pair are exactly open subsets and closed subsets. We also prove that a relation between two sets of points can be communicated faithfully if and only if it is continuous or open. Finally we introduce new notions of point and of continuous function which are communicable.

Keywords: Topology, communication, basic pairs, constructive mathematics

DOI: 10.3233/FI-2020-1963

Journal: Fundamenta Informaticae, vol. 176, no. 1, pp. 61-78, 2020