One of its namesakes has a lemma with Cantelli which states that if the probability for an infinite set of events is 0 if the sum of probabilities for all events is less than infinity, and the other names a theorem about uniform continuity of certain functions along with Cantor.
One of its namesakes has a lemma with Cantelli which states that if the probability for an infinite set of events is 0 if the sum of probabilities for all events is less than infinity, and the other names a theorem about uniform continuity of certain functions along with Cantor. A combinatorial proof for it was developed using finite bitstrings and Brouwer's fan theorem, and was developed by Macauley and Rabern. Tychonoff's theorem yields a result similar to this theorem, and accumulation points for an infinite set A which belong to A have finite covers according to this theorem which can be proved by the Bolzano Weierstrass theorem for real numbers. For 10 points, identify this theorem named after a German and a Frenchman, which states that any subspace which is compact has to be both bounded and closed.
One of its namesakes has a lemma with Cantelli which states that if the probability for an infinite set of events is 0 if the sum of probabilities for all events is less than infinity, and the other names a theorem about uniform continuity of certain functions along with Cantor.
{Heine-Borel} Theorem [accept in either order]