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κ-compactness, extent and the Lindelöf number in LOTS

David Buhagiar, Emmanuel Chetcuti, Hans Weber (2014)

Open Mathematics

We study the behaviour of ℵ-compactness, extent and Lindelöf number in lexicographic products of linearly ordered spaces. It is seen, in particular, that for the case that all spaces are bounded all these properties behave very well when taking lexicographic products. We also give characterizations of these notions for generalized ordered spaces.

ω H-sets and cardinal invariants

Alessandro Fedeli (1998)

Commentationes Mathematicae Universitatis Carolinae

A subset A of a Hausdorff space X is called an ω H-set in X if for every open family 𝒰 in X such that A ⊂ ⋃ 𝒰 there exists a countable subfamily 𝒱 of 𝒰 such that A ⊂ ⋃ { V ¯ : V ∈ 𝒱 } . In this paper we introduce a new cardinal function t s θ and show that | A | ≤ 2 t s θ ( X ) ψ c ( X ) for every ω H-set A of a Hausdorff space X .

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