Cardinal invariants and compactifications

Anatoly A. Gryzlov

Displaying similar documents to “Cardinal invariants and compactifications”

On $π$ -metrizable spaces, their continuous images and products

Derrick Stover (2009)

Commentationes Mathematicae Universitatis Carolinae

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A space $X$ is said to be $π$ -metrizable if it has a $σ$ -discrete $π$ -base. The behavior of $π$ -metrizable spaces under certain types of mappings is studied. In particular we characterize strongly $d$ -separable spaces as those which are the image of a $π$ -metrizable space under a perfect mapping. Each Tychonoff space can be represented as the image of a $π$ -metrizable space under an open continuous mapping. A question posed by Arhangel’skii regarding if a $π$ -metrizable topological group must be metrizable...

$𝒫$ -approximable compact spaces

Mihail G. Tkachenko (1991)

Commentationes Mathematicae Universitatis Carolinae

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For every topological property $𝒫$ , we define the class of $𝒫$ -approximable spaces which consists of spaces X having a countable closed cover $γ$ such that the “section” $X (x, γ) = ⋂ {F \in γ : x \in F}$ has the property $𝒫$ for each $x \in X$ . It is shown that every $𝒫$ -approximable compact space has $𝒫$ , if $𝒫$ is one of the following properties: countable tightness, $ℵ_{0}$ -scatteredness with respect to character, $C$ -closedness, sequentiality (the last holds under MA or $2^{ℵ_{0}} < 2^{ℵ_{1}}$ ). Metrizable-approximable spaces are studied: every compact space in...

Convergence in compacta and linear Lindelöfness

Aleksander V. Arhangel&#039;skii, Raushan Z. Buzyakova (1998)

Commentationes Mathematicae Universitatis Carolinae

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Let $X$ be a compact Hausdorff space with a point $x$ such that $X ∖ {x}$ is linearly Lindelöf. Is then $X$ first countable at $x$ ? What if this is true for every $x$ in $X$ ? We consider these and some related questions, and obtain partial answers; in particular, we prove that the answer to the second question is “yes” when $X$ is, in addition, $ω$ -monolithic. We also prove that if $X$ is compact, Hausdorff, and $X ∖ {x}$ is strongly discretely Lindelöf, for every $x$ in $X$ , then $X$ is first countable. An example of linearly...

Displaying similar documents to “Cardinal invariants and compactifications”

On π -metrizable spaces, their continuous images and products

𝒫 -approximable compact spaces

Convergence in compacta and linear Lindelöfness

On $π$ -metrizable spaces, their continuous images and products

$𝒫$ -approximable compact spaces