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

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 → ℝ is continuous at a point x iff f is sequentially continuous...

Convergence in compacta and linear Lindelöfness

Aleksander V. Arhangel'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...