Generalized continuous closure spaces I

Meet preserving closure operations

verfasst von

Marcel Erné

Abstract

We study general notions of convergence and continuity in arbitrary spaces or ordered sets, extending considerably topological concepts in domain theory like those of Scott convergence, alias lower (lim-inf) convergence, and Scott topology. It turns out that the convergence-theoretical properties of being localized, a limit relation, pretopological, or topological, respectively, all correspond to important properties of the underlying ordered sets that reduce to (meet) continuity and similar properties in the classical situation. Basic tools are the cut closure operators and diverse order-theoretical or topological variants of them. We characterize the generalized Scott convergence spaces abstractly as so-called core determined convergence spaces. This unifying concept provides simplifications and new insights into various areas of order theory, topology and theoretical computer science. In particular, some intimate connections between convergence properties, meet preservation by certain closure operations, and the continuity of meet operations are established.

Organisationseinheit(en)

Institut für Algebra, Zahlentheorie und Diskrete Mathematik

Typ

Artikel

Journal

Topology and its applications

Band

273

ISSN

0166-8641

Publikationsdatum

15.03.2020

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Geometrie und Topologie

Elektronische Version(en)

https://doi.org/10.1016/j.topol.2019.106981 (Zugang: Offen)