M.E. Rudin's proof of Stone's theorem begins with well-ordering an open cover. Good, Tree, and Watson, being set theorists and thus naturally suspiscious of such a move, investigated whether the axiom of choice was necessary for Stone's theorem to be true. In 1996 they showed that in a certain choiceless universe there is a metric space which is not paracompact: a counter-example to Stone's theorem. We will be loosely following their presentation and will prove the same result.
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