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Ideals in Heyting Semilattices and Open Homomorphisms
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jorge Picado Aleš Pultr Anna TozziSubfitness and its relation to openness and completeness is studied in the context of Heyting semilattices. A formally weaker condition (c-subfitness) is shown to be necessary and sufficient for openness and completeness to coincide. For a large class of spatial... -
Universal specialization semilattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Paolo Lipparini --- Università di Roma “Tor Vergata”, ItalyA 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... -
Epimorphisms and closure operators of categories of semilattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: D. Dikranjan --- Università degli Studi di Udine, Italy A. Giordano Bruno --- Università degli Studi di Udine, Italy N. Zava --- Institute of Science and Technology Austria (ISTA),Motivated by a problem posed in [10], we investigate the closure operators of the category SLatt of join semilattices and its subcategory SLatt O of join semilattices with bottom element. In particular, we show that there are only finitely many... -
Some properties of conjunctivity (subfitness) in generalized settings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: M. Andrew Moshier --- CECAT, Chapman University, USA Jorge Picado --- University of Coimbra, Portugal Aleš Pultr --- Charles University, Czech RepublicThe property of subfitness used in point-free topology (roughly speaking) to replace the slightly stronger T 1-separation, appeared (as disjunctivity) already in the pioneering Wallman’s [16], then practically disappeared to reappear again (conjunctivity, subfitness), until it was in the recent...