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this post was submitted on 03 Feb 2026
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Asklemmy
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It wasn't a mistake. Usually you're talking about an infinite-dimensional TVS when you say Banach space - as in it's just Banach, that's the most you can say about it. I don't mean R^3^.
Stuff like the axiom of choice has a way of coming up in functional analysis. Sure, there's weirder spaces, like from general topology or TVS theory in general, but Banach spaces are an example that are pretty widely used and studied. It seems like going with some pathological object I have to search around for would make the point less clear.
The Banach-Tarski paradox wouldn't work either without the AoC, but it's just a specific counterexample, and Banach and Tarski's careers will be fine since they both died decades ago.