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Results tagged with axiom-of-choice
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user 397785
An important and fundamental axiom in set theory sometimes called Zermelo's axiom of choice. It was formulated by Zermelo in 1904 and states that, given any set of mutually disjoint nonempty sets, there exists at least one set that contains exactly one element in common with each of the nonempty sets. The axiom of choice is related to the first of Hilbert's problems.
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Groups $G$ such that $\mathrm{Aut}(G) \simeq \mathbb{Z}/2\mathbb{Z}$
$\DeclareMathOperator\Aut{Aut}\DeclareMathOperator\Inn{Inn}$First I hope my question belongs here, please let me know if it doesn't.
It isn't too hard to show there is no groups $G$ such that $\Aut(G) …
- 69
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Simpler proofs using the axiom of choice
The following theorem, relating path-connectedness and arc-connectedness (arc := injective path):
"Every path-connected Hausdorff space is arc-connected"
can be proven both with the axiom of choice or …