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
Peculiar behavior of connected locales
Pointless uniformities. I. Complete regularity
Pointless uniformities. II: (Dia)metrization
Principal tolerances on lattices
Products of locally connected locales
Quasivarieties of symmetric distributive lattices.
Radical classes of generalized Boolean algebras
Relative bicomplements and tolerance extension property in distributive lattices
Reticulation of a 0-distributive Lattice
A congruence relation on a 0-distributive lattice is defined such that the quotient lattice is a distributive lattice and the prime spectrum of and of are homeomorphic. Also it is proved that the minimal prime spectrum (maximal spectrum) of is homeomorphic with the minimal prime spectrum (maximal spectrum) of .
Saturated Boolean Algebras With Ultrafilters
Saturated Boolean algebras with ultrafilters.
Semilattices of groups with distributive congruence lattice.
Sequential convergences in distributive lattices
In this paper we investigate the system Conv of all sequential convergences on a distributive lattice .