On the resolvability of Lindelöf-generated and (countable extent)-generated spaces

Juhász, István; Soukup, Lajos; Szentmiklóssy, Zoltán

doi:10.1016/j.topol.2019.02.034

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2023

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“…spaces with topology defined by Lindelöf subspaces (Filatova and A.V. Osipov [15], Juhasz, Soukup and Szentmiklossy [16]).…”

Section: Introductionmentioning

confidence: 99%

Resolvability and complete accumulation points

Anton¹

2023

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We prove that: I. For every regular Lindelöf space X if |X| = ∆(X) and cf|X| = ω, then X is maximally resolvable; II. For every regular countably compact space X if |X| = ∆(X) and cf|X| = ω, then X is maximally resolvable.Here ∆(X), the dispersion character of X, is the minimum cardinality of a nonempty open subset of X.Statements I and II are corollaries of the main result: for every regular space X if |X| = ∆(X) and every set A ⊆ X of cardinality cf|X| has a complete accumulation point, then X is maximally resolvable.Moreover, regularity here can be weakened to π-regularity, and the Lindelöf property can be weakened to the linear Lindelöf property.

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“…spaces with topology defined by Lindelöf subspaces (Filatova and A.V. Osipov [15], Juhasz, Soukup and Szentmiklossy [16]).…”

Section: Introductionmentioning

confidence: 99%