Displaying similar documents to “Pure filters and stable topology on BL-algebras”

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 ) = 0 ; (b) for each point x X with nw χ ( x ) = 0 there is an injective sequence ( x n ) n ω in X that -converges to x for some meager filter on ω ; (c) if a functionally Hausdorff space X contains an -convergent injective sequence for some...