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We have proved the Hall's marriage theorem for the finite system of finite sets; now I would like to show that it holds even for infinite system of finite sets.

I have been trying to prove this myself for quite a while, but did not succeed. Can anyone provide a sketch of the proof?

Thanks a lot!

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  • $\begingroup$ Is the theorem known to be true for infinite systems of finite sets? $\endgroup$ – templatetypedef Sep 10 '13 at 22:31
  • $\begingroup$ I suspect yes; but I am not sure. $\endgroup$ – Ondra Hrubý Sep 10 '13 at 22:34
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Hint: Use the Cowan-Engeler Lemma. I put up a full proof on ProofWiki

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