O existenčných algebrách
On complete -algebras
On distributive fixed-point expressions
On Distributive Fixed-Point Expressions
For every fixed-point expression e of alternation-depth r, we construct a new fixed-point expression e' of alternation-depth 2 and size . Expression e' is equivalent to e whenever operators are distributive and the underlying complete lattice has a co-continuous least upper bound. We alternation-depth but also w.r.t. the increase in size of the resulting expression.
On equalizers in the category of frames with weakly open homomorphisms
On paracompact locales and metric locales
On pushing out frames
On the dominance partial ordering of Dyck paths.
On the height of order ideals
We maximize the total height of order ideals in direct products of finitely many finite chains. We also consider several order ideals simultaneously. As a corollary, a shifting property of some integer sequences, including digit sum sequences, is derived.
On the paracompactness of frames
Through the study of frame congruences, new characterizations of the paracompactness of frames are obtained.
On -continuous tolerances of -distributive lattices