Order Maps And Unique Fixed Points In Complete Lattices
Ordres "C.A.C."
Orthomodular lattices and closure operations in ordered vector spaces
On a non-trivial partially ordered real vector space (V,≤) the orthogonality relation is defined by incomparability and ζ(V,⊥) is a complete lattice of double orthoclosed sets. We say that A ⊆ V is an orthogonal set when for all a,b ∈ A with a ≠ b, we have a ⊥ b. In our earlier papers we defined an integrally open ordered vector space and two closure operations A → D(A) and . It was proved that V is integrally open iff for every orthogonal set A ⊆ V. In this paper we generalize this result. We...
Outer measure analysis of topological lattice properties.
Outer measures and associated lattice properties.
Partial dcpo’s and some applications
We introduce partial dcpo’s and show their some applications. A partial dcpo is a poset associated with a designated collection of directed subsets. We prove that (i) the dcpo-completion of every partial dcpo exists; (ii) for certain spaces , the corresponding partial dcpo’s of continuous real valued functions on are continuous partial dcpos; (iii) if a space is Hausdorff compact, the lattice of all S-lower semicontinuous functions on is the dcpo-completion of that of continuous real valued...
Partially ordered sets with projections and their topology [Book]
Partially-additive monoids
Partitions and congruences in algebras. II. Modular and distributive equalities, complements
Partitions and congruences in algebras. III. Commutativity of congruences
Partitions and congruences in algebras. IV. Associable systems
Partitions and partially ordered sets
Perfect compactifications of frames
Perfect compactifications of frames are introduced. It is shown that the Stone-Čech compactification is an example of such a compactification. We also introduce rim-compact frames and for such frames we define its Freudenthal compactification, another example of a perfect compactification. The remainder of a rim-compact frame in its Freudenthal compactification is shown to be zero-dimensional. It is shown that with the assumption of the Boolean Ultrafilter Theorem the Freudenthal compactification...
Perfect Elements in the Free Modular Lattices.
Perfect semilattices.
Permutability, Distributivity of Equivalence Relations and Direct Products
Permutability of congruences in varieties with idempotent operations
Permutability of distributive congruence relations in a joint semilattice directed below
Polarity compatible with a closure system
Polars in autometrized algebras