A note on the product of measure algebras
A note on the symmetric difference in lattices.
The paper introduces a definition of symmetric difference in lattices with negation, presents its general properties and studies those that are typical of ortholattices, orthomodular lattices, De Morgan and Boolean algebras.
A note on the tolerance lattice of atomistic algebraic lattices.
A note on tolerance lattices
A note on tolerance lattices of finite chains
A note on tolerance lattices of products of lattices
A note on topological -posets of fuzzy sets.
A note on topology compatible with the ordering
A note on topology of -continuous posets
-continuous posets are common generalizations of continuous posets, completely distributive lattices, and unique factorization posets. Though the algebraic properties of -continuous posets had been studied by several authors, the topological properties are rather unknown. In this short note an intrinsic topology on a -continuous poset is defined and its properties are explored.
A note on uniserial loops
All ordinal numbers with the following property are found: there exists a loop such that its subloops form a chain of ordinal type .
A note on weak distributivity and continuous restrictions of Borel functions
A partial order in the knot table.
A partial order where all monotone maps are definable
It is consistent that there is a partial order (P,≤) of size such that every monotone function f:P → P is first order definable in (P,≤).
A partically ordered space which is not a Priestely space.
A polynomial characterization of nondistributive modular lattices
A poset hierarchy
This article extends a paper of Abraham and Bonnet which generalised the famous Hausdorff characterisation of the class of scattered linear orders. They gave an inductively defined hierarchy that characterised the class of scattered posets which do not have infinite incomparability antichains (i.e. have the FAC). We define a larger inductive hierarchy κℌ* which characterises the closure of the class of all κ-well-founded linear orders under inversions, lexicographic sums and FAC weakenings. This...
A precedence theorem for semigroups.
A Priestley view of spatialization of frames
A principal congruence identity characterizing the variety of distributive lattices with zero
A principal topology obtained from uninorms
We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a bounded lattice...