| Francisco Javier García-Pacheco†
Abstract: The order topology has been historically defined only for totally ordered sets. Here, the order topology in partially ordered sets will be constructed. Several attempts have been provided in the recent literature on partially ordered groups, rings and modules. This manuscript contains a full construction that provides solid foundational ground to the previous attempts and serves to pay tribute to the topological trajectory of Prof. Ricceri. Keywords: partially ordered set, order topology, semicontinuity. MSC: 06F30. DOI 10.56082/annalsarscimath.2026.1.161 †garcia.pacheco@uca.es, Department of Mathematics, College of Engineering, Marine Science Institute, University of Cadiz, Avda. de la Universidad 10, 11519 Puerto Real, Spain |
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application,
ISSN ONLINE 2066 – 6594
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