Displaying similar documents to “Finite union of H-sets and countable compact sets”

Countably metacompact spaces in the constructible universe

Paul Szeptycki (1993)

Fundamenta Mathematicae

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We present a construction from ♢* of a first countable, regular, countably metacompact space with a closed discrete subspace that is not a G δ . In addition some nonperfect spaces with σ-disjoint bases are constructed.

Lindelöf property and the iterated continuous function spaces

G. Sokolov (1993)

Fundamenta Mathematicae

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We give an example of a compact space X whose iterated continuous function spaces C p ( X ) , C p C p ( X ) , . . . are Lindelöf, but X is not a Corson compactum. This solves a problem of Gul’ko (Problem 1052 in [11]). We also provide a theorem concerning the Lindelöf property in the function spaces C p ( X ) on compact scattered spaces with the ω 1 th derived set empty, improving some earlier results of Pol [12] in this direction.

Semiring of Sets: Examples

Roland Coghetto (2014)

Formalized Mathematics

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This article proposes the formalization of some examples of semiring of sets proposed by Goguadze [8] and Schmets [13].

On D-dimension of metrizable spaces

Wojciech Olszewski (1991)

Fundamenta Mathematicae

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For every cardinal τ and every ordinal α, we construct a metrizable space M α ( τ ) and a strongly countable-dimensional compact space Z α ( τ ) of weight τ such that D ( M α ( τ ) ) ≤ α , D ( Z α ( τ ) ) ≤ α and each metrizable space X of weight τ such that D(X) ≤ α is homeomorphic to a subspace of M α ( τ ) and to a subspace of Z α + 1 ( τ ) .