A compact ccc non-separable space from a Hausdorff gap and Martin's Axiom

Murray G. Bell

Displaying similar documents to “A compact ccc non-separable space from a Hausdorff gap and Martin's Axiom”

Spaces with $σ$ - $n$ -linked topologies as special subspaces of separable spaces

Ronnie Levy, Mikhail Matveev (1999)

Commentationes Mathematicae Universitatis Carolinae

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We characterize spaces with $σ$ - $n$ -linked bases as specially embedded subspaces of separable spaces, and derive some corollaries, such as the $𝐜$ -productivity of the property of having a $σ$ -linked base.

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...

Separable extensions of first countable spaces

Eric van Douwen, Teodor Przymusiński (1980)

Fundamenta Mathematicae

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$𝒫$ -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...

Displaying similar documents to “A compact ccc non-separable space from a Hausdorff gap and Martin's Axiom”

Spaces with σ - n -linked topologies as special subspaces of separable spaces

Convergence in compacta and linear Lindelöfness

Separable extensions of first countable spaces

𝒫 -approximable compact spaces

Spaces with $σ$ - $n$ -linked topologies as special subspaces of separable spaces

$𝒫$ -approximable compact spaces