Products of Lindelöf $T_2$-spaces are Lindelöf – in some models of ZF

Horst Herrlich

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When is $𝐍$ Lindelöf?

Horst Herrlich, George E. Strecker (1997)

Commentationes Mathematicae Universitatis Carolinae

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Theorem. In ZF (i.e., Zermelo-Fraenkel set theory without the axiom of choice) the following conditions are equivalent: (1) $ℕ$ is a Lindelöf space, (2) $ℚ$ is a Lindelöf space, (3) $ℝ$ is a Lindelöf space, (4) every topological space with a countable base is a Lindelöf space, (5) every subspace of $ℝ$ is separable, (6) in $ℝ$ , a point $x$ is in the closure of a set $A$ iff there exists a sequence in $A$ that converges to $x$ , (7) a function $f : ℝ \to ℝ$ is continuous at a point $x$ iff $f$ is sequentially continuous...

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...

Three small results on normal first countable linearly H-closed spaces

Mathieu Baillif (2022)

Commentationes Mathematicae Universitatis Carolinae

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We use topological consequences of , and proved by other authors to show that normal first countable linearly H-closed spaces with various additional properties are compact in these models.

Displaying similar documents to “Products of Lindelöf T 2 -spaces are Lindelöf – in some models of ZF”

When is 𝐍 Lindelöf?

Convergence in compacta and linear Lindelöfness

Three small results on normal first countable linearly H-closed spaces

Displaying similar documents to “Products of Lindelöf $T_{2}$ -spaces are Lindelöf – in some models of ZF”

When is $𝐍$ Lindelöf?