Concerning almost realcompactifications
When is Lindelöf?
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 is in the closure of a set iff there exists a sequence in that converges to , (7) a function is continuous at a point iff is sequentially continuous at , (8)...
Construction of Cartesian closed topological hulls
Least and largest initial completions. II.
Least and largest initial completions. I.
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