20 citations · 30 across the 14 of their papers we have counts for
5 papers · 1 filter
Factorizing the Top-Loc adjunction through positive topologies
Francesco Ciraulo, Tatsuji Kawai, Samuele Maschio
We characterize the category of Sambin's positive topologies as a fibration over the category of locales Loc. The fibration is obtained by applying the Grothendieck construction to…
Presenting de Groot duality of stably compact spaces
Tatsuji Kawai
We give a constructive account of the de Groot duality of stably compact spaces in the setting of strong proximity lattice, a point-free representation of a stably compact space. T…
A continuity principle equivalent to the monotone fan theorem
Tatsuji Kawai
The strong continuity principle reads "every pointwise continuous function from a complete separable metric space to a metric space is uniformly continuous near each compact image.…
Principles of bar induction and continuity on Baire space
Tatsuji Kawai
Brouwer-operations, also known as inductively defined neighbourhood functions, provide a good notion of continuity on Baire space which naturally extends that of uniform continuity…
The principle of pointfree continuity
Tatsuji Kawai, Giovanni Sambin
In the setting of constructive pointfree topology, we introduce a notion of continuous operation between pointfree topologies and the corresponding principle of pointfree continuit…