On relatively almost Lindelöf subsets

Yankui Song

Displaying similar documents to “On relatively almost Lindelöf subsets”

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 $Y \subseteq \bar{⋃ 𝒱}$ . 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.

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 “ $| X | \leq ψ_{c} {(X)}^{t (X)}$ " holds.

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 $K \cup Y$ , 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 $X$ ...