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

Taras O. Banakh; Volodymyr Mykhaylyuk; Lubomyr Zdomsky

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Displaying similar documents to “On meager function spaces, network character and meager convergence in topological spaces”

Some observations on filters with properties defined by open covers

Rodrigo Hernández-Gutiérrez, Paul J. Szeptycki (2015)

Commentationes Mathematicae Universitatis Carolinae

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We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of $𝒫 (ω)$ with the Cantor set topology.

The point of continuity property, neighbourhood assignments and filter convergences

Ahmed Bouziad (2012)

Fundamenta Mathematicae

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We show that for some large classes of topological spaces X and any metric space (Z,d), the point of continuity property of any function f: X → (Z,d) is equivalent to the following condition: (*) For every ε > 0, there is a neighbourhood assignment ${(V_{x})}_{x \in X}$ of X such that d(f(x),f(y)) < ε whenever $(x, y) \in V_{y} \times V_{x}$ . We also give various descriptions of the filters ℱ on the integers ℕ for which (*) is satisfied by the ℱ-limit of any sequence of continuous functions from a topological space into a metric...

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 $({Depth}^{+} ({[ω]}^{ℵ_{0}}) \leq 𝔟)$ . 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 $⋃_{fin} (𝒪, 𝒪)$ .

Guessing clubs in the generalized club filter

Bernhard König, Paul Larson, Yasuo Yoshinobu (2007)

Fundamenta Mathematicae

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We present principles for guessing clubs in the generalized club filter on $_{κ} λ$ . These principles are shown to be weaker than classical diamond principles but often serve as sufficient substitutes. One application is a new construction of a λ⁺-Suslin-tree using assumptions different from previous constructions. The other application partly solves open problems regarding the cofinality of reflection points for stationary subsets of ${[λ]}^{ℵ ₀}$ .

Products of topological spaces and families of filters

Paolo Lipparini (2023)

Commentationes Mathematicae Universitatis Carolinae

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We show that, under suitably general formulations, covering properties, accumulation properties and filter convergence are all equivalent notions. This general correspondence is exemplified in the study of products. We prove that a product is Lindelöf if and only if all subproducts by $\leq ω_{1}$ factors are Lindelöf. Parallel results are obtained for final $ω_{n}$ -compactness, $[λ, μ]$ -compactness, the Menger and the Rothberger properties.

Filter descriptive classes of Borel functions

Gabriel Debs, Jean Saint Raymond (2009)

Fundamenta Mathematicae

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We first prove that given any analytic filter ℱ on ω the set of all functions f on $2^{ω}$ which can be represented as the pointwise limit relative to ℱ of some sequence ${(f ₙ)}_{n \in ω}$ of continuous functions ( $f = l i m_{ℱ} f ₙ$ ), is exactly the set of all Borel functions of class ξ for some countable ordinal ξ that we call the rank of ℱ. We discuss several structural properties of this rank. For example, we prove that any free Π⁰₄ filter is of rank 1.

Some properties of state filters in state residuated lattices

Michiro Kondo (2021)

Mathematica Bohemica

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We consider properties of state filters of state residuated lattices and prove that for every state filter $F$ of a state residuated lattice $X$ : (1) $F$ ...

Displaying similar documents to “On meager function spaces, network character and meager convergence in topological spaces”

Some observations on filters with properties defined by open covers

The point of continuity property, neighbourhood assignments and filter convergences

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

Guessing clubs in the generalized club filter

Products of topological spaces and families of filters

Filter descriptive classes of Borel functions

Some properties of state filters in state residuated lattices

A semifilter approach to selection principles II: $τ^{*}$ -covers