>>235-236より

1）可算選択の公理なしで、コーシー列の収束が言えることと
　上記 fr.wikipedia 可算選択公理における下記の記述とは、矛盾しない と思う
”Theorem 1.1 ([15], [29], [30]). Equivalent are:
1. in R, a point x is an accumulation point of a subset A iff there exists a sequence in A＼{x} that converges to x,
2. a function f : R → R is continuous at a point x iff it is sequentially continuous at x,
3. a real-valued function f : A → R from a subspace A of R is continuous iff it is sequentially continuous,
4. each subspace of R is separable,
5. R is a Lindel¨ of space,
6. Q is a Lindel¨ of space,
7. N is a Lindel¨ of space,
8. each unbounded subset of R contains an unbounded sequence,
9. the Axiom of Choice for countable collections of subsets of R.
There exist models of ZF that violate the above conditions ([17], [18]).
Observe the fine distinction between conditions 2 and 3 of Theorem 1.1.”

2）つまり、可算選択の公理なしで、コーシー列の収束が言えるとして
　その上で、可算選択公理を認めると
”1. in R, a point x is an accumulation point of a subset A iff there exists a sequence in A＼{x} that converges to x,”
”4. each subspace of R is separable,”
”5. R is a Lindel¨ of space,”
　成立！

3）というか、”9. the Axiom of Choice for countable collections of subsets of R.”
　と、Equivalent である！

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