Topology as Faithful Communication Through Relations

• Autorzy: Maschio Samuele , Sambin Giovanni

Identyfikatory

DOI

10.3233/FI-2020-1963

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

basic pairs; communication; constructive mathematics; topology

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2020
• Tom: Vol. 176, nr 1
• Strony: 61--78
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Maschio Samuele

• Dipartimento di Matematica "Tullio Levi-Civita", Università di Padova, Via Trieste 63, 35131 Padova, Italy

autor

Sambin Giovanni

• Dipartimento di Matematica "Tullio Levi-Civita", Università di Padova, Via Trieste 63, 35131 Padova, Italy

Bibliografia

• [1] Sambin G. Some points in formal topology. Theoretical Computer Science, 2003. 305:347-408. URL https://doi.org/10.1016/S0304-3975(02)00704-1.
• [2] Sambin G. Positive Topology and the Basic Picture. New structures emerging from Constructive Mathematics. Oxford University Press. To appear.
• [3] Maietti ME, Sambin G. Toward a minimalist foundation for constructive mathematics. In: L Crosilla and P Schuster (ed.), From Sets and Types to Topology and Analysis: Practicable Foundations for Constructive Mathematics, number 48 in Oxford Logic Guides. Oxford University Press, 2005 pp. 91-114. ISBN-13:9780198566519.
• [4] Maietti ME. A minimalist two-level foundation for constructive mathematics. Annals of Pure and Applied Logic, 2009. 160(3):319-354. URL https://doi.org/10.1016/j.apal.2009.01.006.
• [5] Johnstone PT. Stone Spaces. Cambridge U. P., 1982. ISBN:0521337798, 9780521337793.
• [6] Bergè C. Espace topologiques - functions multivoques. Dunod, Paris, 1959. OCLC:418724771.
• [7] Klein E, Thompson AC. Theory of correspondences. John Wiley & Sons 1984. OCLC:10456617, ISBN:0471880167, 9780471880165.
• [8] Rockafellar RT, Wets RJB. Variational analysis, volume 317 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, 1998. doi:10.1007/978-3-642-02431-3.
• [9] Armstrong M. Basic Topology. Undergraduate Texts in Mathematics. Springer, 1990. doi:10.1007/978-3-642-61265-7.
• [10] Jänich K, Levy S. Topology. Undergraduate Texts in Mathematics. Springer New York, 1995. doi:10.1007/978-3-642-61701-0.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).