Hewitt-Marczewski-Pondiczery theorem

The Hewitt–Marczewski–Pondiczery TheoremMathworldPlanetmath is a result on the density of productsPlanetmathPlanetmathPlanetmath of topological spacesMathworldPlanetmath. This theorem was arrived at independently by Hewitt[1], Marczewski[2] and Pondiczery[3] in the 1940s.


Let κ be an infiniteMathworldPlanetmath cardinal numberMathworldPlanetmath and S an index setMathworldPlanetmathPlanetmath of cardinality at most 2κ. If Xs (sS) are topological spaces with d(Xs)κ then


The special case κ=0 says that the product of at most continuum many separable spacesMathworldPlanetmath is separable.


  • 1 Edwin Hewitt, A remark on density characters, Bull. Amer. Math. Soc. 52 (1946), 641–643. (This paper is available as a PDF file from the AMS website: http://www.ams.org/journals/bull/1946-52-08/home.htmlBull. Amer. Math. Soc., Volume 52, Number 8.)
  • 2 Edward Marczewski, Séparabilité et multiplication cartésienne des espaces topologiques, Fund. Math. 34 (1947), 127–143. (This paper is available as a PDF file from the Polish Virtual Library of Science: http://matwbn.icm.edu.pl/tresc.php?wyd=1&tom=34&jez=enFundamenta Mathematicae, Volume 34.)
  • 3 E. S. Pondiczery, Power problems in abstract spaces, Duke Math. J. 11 (1944), 835–837.
Title Hewitt-Marczewski-Pondiczery theorem
Canonical name HewittMarczewskiPondiczeryTheorem
Date of creation 2013-03-22 17:16:56
Last modified on 2013-03-22 17:16:56
Owner yark (2760)
Last modified by yark (2760)
Numerical id 6
Author yark (2760)
Entry type Theorem
Classification msc 54D65
Classification msc 54A25
Related topic Dense
Related topic Separable