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 deri...
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 ...
The paper studies how the localic notion of sublocale transfers to formal topology. For any formal topology (not necessarily with positivity predicate) we define a sublocale to b...
It is shown that the space X[0,1], of continuous maps [0, 1] X with the compact-open topology, is not locally compact for any space X having a nonconstant path of closed points. ...
This paper uses the locale theory approach to topology. Two descriptions are given of all locale limits, the first description using suplattice constructions and the second prefra...