Displaying similar documents to “Boundary approach filters for analytic functions”

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...

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.

Boundary behaviour of harmonic functions in a half-space and brownian motion

D. L. Burkholder, Richard F. Gundy (1973)

Annales de l'institut Fourier

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Let u be harmonic in the half-space R + n + 1 , n ≥ 2 . We show that u can have a fine limit at almost every point of the unit cubs in R n = ∂ R + n + 1 but fail to have a nontangential limit at any point of the cube. The method is probabilistic and utilizes the equivalence between conditional Brownian motion limits and fine limits at the boundary. In R + 2 it is known that the Hardy classes H p , 0 < p < ∞ , may be described in terms of the integrability of the nontangential maximal function, or, alternatively, in terms...