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Local cardinal functions of H-closed spaces

Angelo Bella, Jack R. Porter (1996)

Commentationes Mathematicae Universitatis Carolinae

The cardinal functions of pseudocharacter, closed pseudocharacter, and character are used to examine H-closed spaces and to contrast the differences between H-closed and minimal Hausdorff spaces. An H-closed space X is produced with the properties that | X | > 2 2 ψ ( X ) and ψ ¯ ( X ) > 2 ψ ( X ) .

Local cohomological properties of homogeneous ANR compacta

V. Valov (2016)

Fundamenta Mathematicae

In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR continuum and x ∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of Ū and bd U are similar to the properties of the closed ball ⁿ ⊂ ℝⁿ and its boundary n - 1 . We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group Hₙ(X,X∖x;ℤ) is not trivial for some x ∈ X. This implies that...

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