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Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras

Jan Paseka, Zdena Riečanová, Junde Wu (2010)


We prove that the interval topology of an Archimedean atomic lattice effect algebra E is Hausdorff whenever the set of all atoms of E is almost orthogonal. In such a case E is order continuous. If moreover E is complete then order convergence of nets of elements of E 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 E corresponding to compact and cocompact elements....

Bohr compactifications of discrete structures

Joan Hart, Kenneth Kunen (1999)

Fundamenta Mathematicae

We prove the following theorem: Given a⊆ω and 1 α < ω 1 C K , if for some η < 1 and all u ∈ WO of length η, a is Σ α 0 ( u ) , then a is Σ α 0 .We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: Σ 1 1 -Turing-determinacy implies the existence of 0 .

Closed ideals in topological algebras: a characterization of the topological Φ -algebra C k ( X )

F. Montalvo, Antonio A. Pulgarín, Batildo Requejo Fernández (2006)

Czechoslovak Mathematical Journal

Let A be a uniformly closed and locally m-convex Φ -algebra. We obtain internal conditions on A stated in terms of its closed ideals for A to be isomorphic and homeomorphic to C k ( X ) , the Φ -algebra of all the real continuous functions on a normal topological space X endowed with the compact convergence topology.

Hyperconvexity of ℝ-trees

W. Kirk (1998)

Fundamenta Mathematicae

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.

More on ordinals in topological groups

Aleksander V. Arhangel'skii, Raushan Z. Buzyakova (2008)

Commentationes Mathematicae Universitatis Carolinae

Let τ be an uncountable regular cardinal and G a T 1 topological group. We prove the following statements: (1) If τ is homeomorphic to a closed subspace of G , G is Abelian, and the order of every non-neutral element of G is greater than 5 then τ × τ embeds in G as a closed subspace. (2) If G is Abelian, algebraically generated by τ G , and the order of every element does not exceed 3 then τ × τ is not embeddable in G . (3) There exists an Abelian topological group H such that ω 1 is homeomorphic to a closed subspace...

On convergence theory in fuzzy topological spaces and its applications

Nouh, Ali Ahmed (2005)

Czechoslovak Mathematical Journal

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 Q -relation and the Q -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 Q -compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar...

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