A universal characterization of the double powerlocale

The Double Powerlocale and Exponentiation: a Case Study in Geometric Logic

If X is a locale, then its double powerlocale PX is defined to be PU(PL(X)) where PU and PL are the upper and lower powerlocale constructions. We prove various results relating it to exponentiation of locales, including the following. First, if X is a locale for which the exponential S exists (where S is the Sierpinski locale), then PX is an exponential S X . Second, if in addition W is a local...

Compactness in locales and in formal topology

If a locale is presented by a “flat site”, it is shown how its frame can be presented by generators and relations as a dcpo. A necessary and sufficient condition is derived for compactness of the locale (and also for its openness). Although its derivation uses impredicative constructions, it is also shown predicatively using the inductive generation of formal topologies. A predicative proof of ...

The study of African horsesickness virus by the agar double-diffusion precipitation test. Characterization of the precipitation antigen

The universal $mathcal{AIR}$- compactification of a semigroup

In this paper we establish a characterization of abelian compact Hausdorff semigroups with unique idempotent and ideal retraction property. We also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal withrespect to these properties.

Constructive points of Powerlocales

Results of Bunge and Funk and of Johnstone, providing constructively sound descriptions of the global points of the lower and upper powerlocales, are extended here to describe the generalized points and proved in a way that displays in a symmetric fashion two complementary treatments of frames: as suplattices and as preframes. We then also describe the points of the Vietoris powerlocale. In eac...