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  1. Sep 2024
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    Elementary Topology, 2nd ed. Michael C. Gemignani
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    1. chrisaldrich 30 Sep 2024
      Z orn ’s lemma. Suppose S, < is a partially ordered set with the property that every chain in S has an upper bound. Then S contains amaximal element.

      typo : < should be ≤

      Zorn's lemma lemmas partially ordered sets axiom of choice definitions
    2. chrisaldrich 30 Sep 2024
      The axiom o f choice. Suppose {Si}, i E I, is a family of nonemptysets. Then there is a function / from I into U / Si such that f(i) E Sifor each i e I.

      For any collection of non-empty sets, one can create a set by choosing one element from each set in the given collection.

      There are a variety of other equivalent ways to state this as well as names. One variation is Zorn's lemma.

      axiom of choice Zorn's lemma definitions

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