Displaying similar documents to “A type of βN with ℵ 0 relative types”

On relatively almost countably compact subsets

Yan-Kui Song, Shu-Nian Zheng (2010)

Mathematica Bohemica

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A subset Y of a space X is almost countably compact in X if for every countable cover 𝒰 of Y by open subsets of X , there exists a finite subfamily 𝒱 of 𝒰 such that Y ⊆ ⋃ 𝒱 ¯ . In this paper we investigate the relationship between almost countably compact spaces and relatively almost countably compact subsets, and also study various properties of relatively almost countably compact subsets.

An example of a space whose all continuous mappings are almost injective

Pablo Mendoza Iturralde (2001)

Commentationes Mathematicae Universitatis Carolinae

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We show that all continuous maps of a space X onto second countable spaces are pseudo-open if and only if every discrete family of nonempty G δ -subsets of X is finite. We also prove under CH that there exists a dense subspace X of the real line ℝ , such that every continuous map of X is almost injective and X cannot be represented as K ∪ Y , where K is compact and Y is countable. This partially answers a question of V.V. Tkachuk in [Tk]. We show that for a compact X , all continuous maps of X ...

Almost disjoint families and property (a)

Paul Szeptycki, Jerry Vaughan (1998)

Fundamenta Mathematicae

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We consider the question: when does a Ψ-space satisfy property (a)? We show that if | A | < p then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality p which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a). ...

Special almost P-spaces

Alessandro Fedeli (1997)

Commentationes Mathematicae Universitatis Carolinae

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Motivated by some examples, we introduce the concept of special almost P-space and show, using the reflection principle, that for every space X of this kind the inequality “ | X | ≤ ψ c ( X ) t ( X ) " holds.