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θ -regular spaces.

Janković, Dragan S. (1985)

International Journal of Mathematics and Mathematical Sciences

Σ -products and selections of set-valued mappings

Ivailo Shishkov (2001)

Commentationes Mathematicae Universitatis Carolinae

Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 Y , where X is a Σ -product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

Σ s -products revisited

Reynaldo Rojas-Hernández (2015)

Commentationes Mathematicae Universitatis Carolinae

We show that any Σ s -product of at most 𝔠 -many L Σ ( ≤ ω ) -spaces has the L Σ ( ≤ ω ) -property. This result generalizes some known results about L Σ ( ≤ ω ) -spaces. On the other hand, we prove that every Σ s -product of monotonically monolithic spaces is monotonically monolithic, and in a similar form, we show that every Σ s -product of Collins-Roscoe spaces has the Collins-Roscoe property. These results generalize some known results about the Collins-Roscoe spaces and answer some questions due to Tkachuk [Lifting the Collins-Roscoe...

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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