Displaying similar documents to “Monomorphisms in spaces with Lindelöf filters”

Frame monomorphisms and a feature of the l -group of Baire functions on a topological space

Richard N. Ball, Anthony W. Hager (2013)

Commentationes Mathematicae Universitatis Carolinae

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“The kernel functor” W → k LFrm from the category W of archimedean lattice-ordered groups with distinguished weak unit onto LFrm, of Lindelöf completely regular frames, preserves and reflects monics. In W , monics are one-to-one, but not necessarily so in LFrm. An embedding ϕ ∈ W for which k ϕ is one-to-one is termed kernel-injective, or KI; these are the topic of this paper. The situation is contrasted with kernel-surjective and -preserving (KS and KP). The W -objects every embedding of which is KI...

On meager function spaces, network character and meager convergence in topological spaces

Taras O. Banakh, Volodymyr Mykhaylyuk, Lubomyr Zdomsky (2011)

Commentationes Mathematicae Universitatis Carolinae

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For a non-isolated point x of a topological space X let nw χ ( x ) be the smallest cardinality of a family 𝒩 of infinite subsets of X such that each neighborhood O ( x ) ⊂ X of x contains a set N ∈ 𝒩 . We prove that (a) each infinite compact Hausdorff space X contains a non-isolated point x with nw χ ( x ) = ℵ 0 ; (b) for each point x ∈ X with nw χ ( x ) = ℵ 0 there is an injective sequence ( x n ) n ∈ ω in X that ℱ -converges to x for some meager filter ℱ on ω ; (c) if a functionally Hausdorff space X contains an ℱ -convergent injective sequence for some...

A semifilter approach to selection principles II: τ * -covers

Lubomyr Zdomsky (2006)

Commentationes Mathematicae Universitatis Carolinae

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Developing the idea of assigning to a large cover of a topological space a corresponding semifilter, we show that every Menger topological space has the property ⋃ fin ( 𝒪 , T * ) provided ( 𝔲 < 𝔤 ) , and every space with the property ⋃ fin ( 𝒪 , T * ) is Hurewicz provided ( Depth + ( [ ω ] ℵ 0 ) ≤ 𝔟 ) . Combining this with the results proven in cited literature, we settle all questions whether (it is consistent that) the properties P and Q [do not] coincide, where P and Q run over ⋃ fin ( 𝒪 , Γ ) , ⋃ fin ( 𝒪 , T ) , ⋃ fin ( 𝒪 , T * ) , ⋃ fin ( 𝒪 , Ω ) , and ⋃ fin ( 𝒪 , 𝒪 ) .

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 ...