Description:
Form 341 implies Form 10
Content:
A proof that
Form 341 implies Form 10.
Form 341 states: Every Lindelöf metric space is second countable, and Form 10 is: \(C(\aleph_{0},< \aleph_{0})\): Every countable family of non-empty finite sets has a choice function. Let \(A =\{A_i: i\in\omega\}\), where each \(A_i\) is finite and the \(A_i\)'s are pairwise disjoint. Let \(X\) be the one point compactification of \(\bigcup A\) with the discrete topology. The space \(X\) is Lindelöf, so by Form 341, \(X\) is second countable. This implies that \(\bigcup A\) is countable, which implies there is a choice function on \(A\).
Howard-Rubin number:
158
Type:
Proof
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