Displaying similar documents to “Frame monomorphisms and a feature of the l -group of Baire functions on a topological space”

Monomorphisms in spaces with Lindelöf filters

Richard N. Ball, Anthony W. Hager (2007)

Czechoslovak Mathematical Journal

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𝐒𝐩𝐅𝐢 is the category of spaces with filters: an object is a pair ( X , ℱ ) , X a compact Hausdorff space and ℱ a filter of dense open subsets of X . A morphism f ( Y , 𝒢 ) → ( X , ℱ ) is a continuous function f Y → X for which f - 1 ( F ) ∈ 𝒢 whenever F ∈ ℱ . This category arises naturally from considerations in ordered algebra, e.g., Boolean algebra, lattice-ordered groups and rings, and from considerations in general topology, e.g., the theory of the absolute and other covers, locales, and frames, though we shall specifically...

The H S P -Classes of Archimedean l -groups with Weak Unit

Bernhard Banaschewski, Anthony Hager (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

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W denotes the class of abstract algebras of the title (with homomorphisms preserving unit). The familiar H , S , and P from universal algebra are here meant in W . ℤ and ℝ denote the integers and the reals, with unit 1, qua W -objects. V denotes a non-void finite set of positive integers. Let 𝒢 ⊆ W be non-void and not { { 0 } } . We show ...

A poset of topologies on the set of real numbers

Vitalij A. Chatyrko, Yasunao Hattori (2013)

Commentationes Mathematicae Universitatis Carolinae

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On the set ℝ of real numbers we consider a poset 𝒫 τ ( ℝ ) (by inclusion) of topologies τ ( A ) , where A ⊆ ℝ , such that A 1 ⊇ A 2 iff τ ( A 1 ) ⊆ τ ( A 2 ) . The poset has the minimal element τ ( ℝ ) , the Euclidean topology, and the maximal element τ ( ∅ ) , the Sorgenfrey topology. We are interested when two topologies τ 1 and τ 2 (especially, for τ 2 = τ ( ∅ ) ) from the poset define homeomorphic spaces ( ℝ , τ 1 ) and ( ℝ , τ 2 ) . In particular, we prove that for a closed subset A of ℝ the space ( ℝ , τ ( A ) ) is homeomorphic to the Sorgenfrey line ( ℝ , τ ( ∅ ) ) iff A is countable. We study also common...

Rudin-like sets and hereditary families of compact sets

Étienne Matheron, Miroslav Zelený (2005)

Fundamenta Mathematicae

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We show that a comeager Π₁¹ hereditary family of compact sets must have a dense G δ subfamily which is also hereditary. Using this, we prove an “abstract” result which implies the existence of independent ℳ ₀-sets, the meagerness of ₀-sets with the property of Baire, and generalizations of some classical results of Mycielski. Finally, we also give some natural examples of true F σ δ sets.

Insertion of a Contra-Baire- 1 (Baire- . 5 ) Function

Majid Mirmiran (2019)

Communications in Mathematics

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Necessary and sufficient conditions in terms of lower cut sets are given for the insertion of a Baire- . 5 function between two comparable real-valued functions on the topological spaces that F σ -kernel of sets are F σ -sets.