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Results tagged with big-list
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user 10901
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.
5
votes
What is your favorite proof of Tychonoff's Theorem?
I'm surprised that nobody has mentioned the proof using universal nets. (It can be found, e.g., in Pedersen's 'Analysis NOW' and in Bredon's 'Topology and geometry'.)
A universal net in a set X is a …
4
votes
What is your favorite proof of Tychonoff's Theorem?
I have been teaching general topology for several years, but remained unsatisfied by the proofs given in the books that I based the course upon. Finally I wound up writing my own lecture notes, still …
2
votes
Applications of Brouwer's fixed point theorem
The Perron-Frobenius theorem (in various degrees of generality) is an easy consequence of Brouwer's fixed-point theorem.