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  1. en.wikipedia.org › wiki › Metric_spaceMetric space - Wikipedia

    12 hours ago · Informally, a metric space is complete if it has no "missing points": every sequence that looks like it should converge to something actually converges. To make this precise: a sequence (x n) in a metric space M is Cauchy if for every ε > 0 there is an integer N such that for all m, n > N, d(x m, x n) < ε.

  2. en.wikipedia.org › wiki › Emmy_NoetherEmmy Noether - Wikipedia

    12 hours ago · An example of this is her close work with Wolfgang Krull, who greatly advanced commutative algebra with his Hauptidealsatz and his dimension theory for commutative rings. Another is Gottfried Köthe, who contributed to the development of the theory of hypercomplex quantities using Noether and Krull's methods.

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