A specialization semilattice is a structure which can be embedded into (P(X),∪,⊑), 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. In general, closure is not expressible in a specialization semilattice. On the other hand, we show that every specialization semilattice can be canonically embedded into a "principal" specialization semilattice in which closure can be actually defined.
Lipparini, P. (2022). Universal specialization semilattices. QUAESTIONES MATHEMATICAE, 1-14 [10.2989/16073606.2022.2126805].
Universal specialization semilattices
Paolo Lipparini
2022-01-01
Abstract
A specialization semilattice is a structure which can be embedded into (P(X),∪,⊑), 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. In general, closure is not expressible in a specialization semilattice. On the other hand, we show that every specialization semilattice can be canonically embedded into a "principal" specialization semilattice in which closure can be actually defined.| File | Dimensione | Formato | |
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