The Marriage Problem*

  • Paul R. Halmos
  • Herbert E. Vaughan
Part of the Modern Birkhäuser Classics book series (MBC)


In a recent issue of this journal Weyl1 proved a combinatorial lemma which was apparently considered first by P. Hall2 Subsequently Everett and Whaples 3 published another proof and a generalization of the same lemma. Their proof of the generalization appears to duplicate the usual proof of Tychonoff’s theorem.4 The purpose of this note is to simplify the presentation by employing the statement rather than the proof of that result. At the same time we present a somewhat simpler proof of the original Hall lemma.


Induction Hypothesis Simple Proof Hausdorff Space Recent Issue Finite Union 

Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Paul R. Halmos
    • 1
  • Herbert E. Vaughan
    • 2
  1. 1.University of ChicagoChicagoUSA
  2. 2.University of IllinoisChicagoUSA

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