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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

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What is your favorite proof of Tychonoff's Theorem?

I guess that the proof from Munkres' book is essentially the same as this one due to Loomis. For those who prefer the ultrafilter proof, well, indeed this is the very same proof, because "maximal fami …