$K_\sigma $-bounded sets and filters on $\omega $

Louveau, A.

Displaying similar documents to “ $K_{σ}$ -bounded sets and filters on $ω$ ”

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 $O (x) \subset X$ of $x$ contains a set $N \in 𝒩$ . 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 $x \in X$ with ${nw}_{χ} (x) = ℵ_{0}$ there is an injective sequence ${(x_{n})}_{n \in ω}$ 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...

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.

On the extensibility of closed filters in T $_{1}$ spaces and the existence of well orderable filter bases

Kyriakos Keremedis, Eleftherios Tachtsis (1999)

Commentationes Mathematicae Universitatis Carolinae

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We show that the statement CCFC = “” is equivalent to the CMC and, the axiom of choice AC is equivalent to the statement CFE $_{0}$ = “”. We also show that AC is equivalent to each of the assertions: “”, “” and “”.

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 ${[λ]}^{ℵ ₀}$ .

Displaying similar documents to “ K σ -bounded sets and filters on ω ”

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

Some observations on filters with properties defined by open covers

On the extensibility of closed filters in T 1 spaces and the existence of well orderable filter bases

Guessing clubs in the generalized club filter

Displaying similar documents to “ $K_{σ}$ -bounded sets and filters on $ω$ ”

On the extensibility of closed filters in T $_{1}$ spaces and the existence of well orderable filter bases