A topological lattice on the set of multifunctions.
Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras
We prove that the interval topology of an Archimedean atomic lattice effect algebra is Hausdorff whenever the set of all atoms of is almost orthogonal. In such a case is order continuous. If moreover is complete then order convergence of nets of elements of is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible with a uniformity induced by a separating function family on corresponding to compact and cocompact elements....
Another look at the localic Tychonoff theorem
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 .
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.
Complete distributivity and -convergence
Completion of a class of topological semilattices, applications. (Complétion d'une classe de demi-treillis topologiques, applications.)
Eine Kennzeichnung topologischer Räume durch Vervollständigungen.
Embedding ordered topological spaces into topological semilattices.
Essentially Complete T...-Spaces.
Essentially Complete T...-Spaces II. A Lattice-Theoretic Approach.
Fuzzy filter spectrum of a BCK algebra.
Hyperconvexity of ℝ-trees
It is shown that for a metric space (M,d) the following are equivalent: (i) M is a complete ℝ-tree; (ii) M is hyperconvex and has unique metric segments.
Lattice operators and topologies.
Local convexity in topological lattices
Measurable Refinement Monoids and Applications to Distributive Semilattices, Heyting Algebras, and Stone Spaces.
More on ordinals in topological groups
Let be an uncountable regular cardinal and a topological group. We prove the following statements: (1) If is homeomorphic to a closed subspace of , is Abelian, and the order of every non-neutral element of is greater than then embeds in as a closed subspace. (2) If is Abelian, algebraically generated by , and the order of every element does not exceed then is not embeddable in . (3) There exists an Abelian topological group such that is homeomorphic to a closed subspace...
-абсолют и интегрируемые по Риману функции.
On barely continuous functions.
On convergence theory in fuzzy topological spaces and its applications
In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the -relation and the -neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong -compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar...