Displaying similar documents to “On relatively almost countably compact subsets”

On relatively almost Lindelöf subsets

Yankui Song (2009)

Mathematica Bohemica

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A subspace Y of a space X is almost Lindelöf (strongly almost Lindelöf) in X if for every open cover 𝒰 of X (of Y by open subsets of X ), there exists a countable subset 𝒱 of 𝒰 such that Y ⊆ ⋃ { V ¯ V ∈ 𝒱 } . In this paper we investigate the relationships between relatively almost Lindelöf subset and relatively strongly almost Lindelöf subset by giving some examples, and also study various properties of relatively almost Lindelöf subsets and relatively strongly almost Lindelöf 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 * realcompactness

John J. Schommer, Mary Anne Swardson (2001)

Commentationes Mathematicae Universitatis Carolinae

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We provide a new generalization of realcompactness based on ultrafilters of cozero sets and contrast it with almost realcompactness.

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.