Research Article

Universal specialization semilattices

Published in: Quaestiones Mathematicae
Volume 46 , issue 10 , 2023 , pages: 2163–2176

DOI: 10.2989/16073606.2022.2126805

Author(s): Paolo Lipparini Università di Roma “Tor Vergata”, Italy

Keywords: Primary: 06A15 , Secondary: 54A05 , 06A12 , Specialization semilattice , closure semilattice , closure space , universal extension

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Abstract

A specialization semilattice is a structure which can be embedded into , where X is a topological space, x ⊑ y means x ⊆ Ky, for x, y ⊆ X, and K is closure in X. Specialization semilattices and posets appear as auxiliary structures in many disparate scientific fields, even unrelated to topology.

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