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answered Properties of open covers
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comment A problem on infinite dimensional metric space
As a math.SE moderator I have closed the math.SE version of this question. It this is deemed inappropriate for MO, leave a comment to me on the math.SE question of this question and I/we can re-open it there.
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comment Bijective-equivalent collections of proper classes in set theory
What sort of axiomatization are you thinking of for NBG/MK? I think the most common axiomatizations include (or imply) Limitation of Size, which says that a class is proper iff it admits an injection from V, and from which you then get Global Choice.
Feb
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comment How to see such space is Lindelof?
@John: Do you mean my characterisation of the open subsets of $\mathbb{R}_B$? (Which follows from the fact that the topology generated by the usual open subsets of $\mathbb{R}$ and the singletons from $B$.) Or that there is a countable $I_0$? (Which follows from the fact that $\mathbb{R}$ is second-countable, and thus hereditary Lindelöf.)
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answered How to see such space is Lindelof?
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answered Existence of weakly compact cardinals
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revised A function that is defined everywhere but has unknown values
added 134 characters in body; deleted 1 characters in body
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answered A function that is defined everywhere but has unknown values