A continuous lattice L with DID(L) incomplete.
A maximal chain approach to topology and order.
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 partically ordered space which is not a Priestely space.
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...
An observation on Krull and derived dimensions of some topological lattices
Let , be an algebraic lattice. It is well-known that with its topological structure is topologically scattered if and only if is ordered scattered with respect to its algebraic structure. In this note we prove that, if is a distributive algebraic lattice in which every element is the infimum of finitely many primes, then has Krull-dimension if and only if has derived dimension. We also prove the same result for , the set of all prime elements of . Hence the dimensions on the lattice...
Bohr compactifications of discrete structures
We prove the following theorem: Given a⊆ω and , if for some and all u ∈ WO of length η, a is , then a is .We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: -Turing-determinacy implies the existence of .
Bourbaki's Fixpoint Lemma reconsidered
A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chain-complete partially ordered sets is presented to obtain a condition for one closure system in a complete lattice to be stable under another closure operator of . This is then used to deal with coproducts and other aspects of frames.
Closed ideals in topological algebras: a characterization of the topological -algebra
Let be a uniformly closed and locally m-convex -algebra. We obtain internal conditions on stated in terms of its closed ideals for to be isomorphic and homeomorphic to , the -algebra of all the real continuous functions on a normal topological space endowed with the compact convergence topology.
Compact pospaces
Posets with property DINT which are compact pospaces with respect to the interval topologies are characterized.
Compactifications of partially ordered sets
Completeness in semi-local ideal lattices
Completion of a class of topological semilattices, applications. (Complétion d'une classe de demi-treillis topologiques, applications.)
Connectivity properties of sequential Boolean algebras
Continuity and Extension of Valuations
Control and separating points of modular functions
Generating methods for principal topologies on bounded lattices
In this paper, some generating methods for principal topology are introduced by means of some logical operators such as uninorms and triangular norms and their properties are investigated. Defining a pre-order obtained from the closure operator, the properties of the pre-order are studied.
Graph topologies and uniform convergence in quasi-uniform spaces.
Intrinsic topologies on semilattices of finite breadth.
Lattice operators and topologies.