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!

  • $\begingroup$ 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

Hint: Use the Cowan-Engeler Lemma. I put up a full proof on ProofWiki


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.