text: This statement's demonstration of the existence of a Hamel basis allows for non-linear solutions toCauchy's functional equation.
full_question: This statement's demonstration of the existence of a Hamel basis allows for non-linear solutions toCauchy's functional equation. This statement is equivalent to Tychonoff's theorem, the fact that the product ofany number of compact spaces is compact, or to the fact that any vector space has a basis. In graph theory, thisfact allows for the finding of a spanning tree in any connected graph. It means that, given a partially orderedset where every chain has an upper bound, there is a maximal element, a statement known as Zorn's lemma.It's often combined with the Zermelo-Fraenkel set theory axioms to create ZFC. For 10 points, identify thisaxiom which, informally, says that one can select from a given collection of objects. 
first_sentence: This statement's demonstration of the existence of a Hamel basis allows for non-linear solutions toCauchy's functional equation.
raw_answer: axiom of choice [accept anything mentioned in the question before it is mentioned, since they are all equivalent] 