semi-regular locales are extensions of the classical semiregularspaces. we investigate the conditions such that semi-regularizationis a functor. we also investigate the conditions such that semi-regularizationis a reflection or coreflection.

Semi-regular locales are extensions of the classical semiregular spaces. We investigate the conditions such that semi-regularization is a functor. We also investigate the conditions such that semi-regularization is a reflection or coreflection.

Locatedness is one of the fundamental notions in constructive mathematics. The existence of a positivity predicate on a locale, i.e. the locale being overt, or open, has proved to be fundamental in constructive locale theory. We show that the two notions are intimately connected. Bishop defines a metric space to be compact if it is complete and totally bounded. A subset of a totally bounded set...

What is a computable set? One may call a bounded subset of the plane computable if it can be drawn at any resolution on a computer screen. Using the constructive approach to computability one naturally considers totally bounded subsets of the plane. We connect this notion with notions introduced in other frameworks. A subset of a totally bounded set is again totally bounded iff it is located. L...

We construct a homeomorphism between the compact regular locale of integrals on a Riesz space and the locale of (valuations) on its spectrum. In fact, we construct two geometric theories and show that they are biinterpretable. The constructions are elementary and mostly consist of explicit manipulations on a distributive lattice associated to a given Riesz space.

We formalize new decision procedures for WS1S, M2L(Str), and Presburger Arithmetics. Formulas of these logics denote regular languages. Unlike traditional decision procedures, we do not translate formulas into automata (nor into regular expressions), at least not explicitly. Instead we devise notions of derivatives (inspired by Brzozowski derivatives for regular expressions) that operate on for...

We create an open multilingual wordnet with large wordnets for over 26 languages and smaller ones for 57 languages. It is made by combining wordnets with open licences, data from Wiktionary and the Unicode Common Locale Data Repository. Overall there are over 2 million senses for over 100 thousand concepts, linking over 1.4 million words in hundreds of languages.

Any functor from the category of C*-algebras to the category of locales which assigns to each commutative C*-algebra its Gelfand spectrum must be trivial on algebras of n-by-n matrices for n ≥ 3. The same obstruction applies to the Zariski, Stone, and Pierce spectra. The possibility of spectra in categories other than that of locales is briefly discussed. A recent article [7] by Reyes shows tha...