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Jan 4, 2020 at 21:00 comment added Robert Furber All mentions of sequential compactness in that book are for pseudometric spaces, or the special case of $\mathbb{R}$, and it is stated there, as part of the proof of Proposition 3.26, that under ZF compact implies sequentially compact for pseudometric spaces, without any form of choice. As the question is about finding compact spaces that are not sequentially compact, this does not resolve the problem.
Jun 25, 2013 at 3:02 review Late answers
Jun 25, 2013 at 12:45
Feb 19, 2013 at 13:44 comment added Gerald Edgar How about a page number of the book? Or is the whole book on this one question?
Feb 19, 2013 at 8:41 history answered sgarde CC BY-SA 3.0