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When is 𝐍 Lindelöf?

Horst HerrlichGeorge E. Strecker — 1997

Commentationes Mathematicae Universitatis Carolinae

Theorem. In ZF (i.e., Zermelo-Fraenkel set theory without the axiom of choice) the following conditions are equivalent: (1) is a Lindelöf space, (2) is a Lindelöf space, (3) is a Lindelöf space, (4) every topological space with a countable base is a Lindelöf space, (5) every subspace of is separable, (6) in , 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 : is continuous at a point x iff f is sequentially continuous at x , (8)...

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