We provide a direct and elementary proof of the fact that the category of Nachbin's compact
ordered spaces is dually equivalent to an ℵ _1 ℵ 1-ary variety of algebras. Further, we show …

We provide a characterisation of the category KH of compact Hausdorff spaces and
continuous maps by means of categorical properties only. To this aim we introduce a notion …

A common feature of many duality results is that the involved equivalence functors are
liftings of hom-functors into the two-element space resp. lattice. Due to this fact, we can only …

It is known since the late 1960's that the dual of the category of compact Hausdorff spaces
and continuous maps is a variety--not finitary, but bounded by $\aleph_1 $. In this note we …

We prove that the category of Nachbin's compact ordered spaces and order-preserving
continuous maps between them is dually equivalent to a variety of algebras, with operations …

In a recent paper (2018), D. Hofmann, R. Neves and P. Nora proved that the dual of the
category of compact partially ordered spaces and monotone continuous maps is a quasi …

Following Bratteli's original definition, an AF-algebra A is the norm closure of the union of an
ascending sequence of finite-dimensional C⁎-algebras, all with the same unit. Elliott proved …

We show that no faithful functor from the category of Hilbert spaces with linear isometries
into the category of sets preserves directed colimits. Thus Hilbert spaces cannot form an …

We extend Łukasiewicz logic obtaining the infinitary logic Infinitary Riesz Logic (Ł) whose
models are algebras C (X,[0, 1]), where X is a basically disconnected compact Hausdorff …

We prove a number of dualities between posets and (pseudo) bases of open sets in locally
compact Hausdorff spaces. In particular, we show that (1) Relatively compact basic …