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A proof that there exists an infinite collection of sets whose cartesian product is nonempty.

I stumbled upon this succinct proof while discussing topology with some friends. Suppose that, for any infinite collection of sets , the cartesian product, i.e. the collection of all choice functions on , is empty. I claim this implies Tychonoff’s theorem, which states that the product of any collection of compact topological spaces is aContinue reading “A proof that there exists an infinite collection of sets whose cartesian product is nonempty.”

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