Hewitt-Marczewski-Pondiczery theorem
The Hewitt–Marczewski–Pondiczery Theorem is a result on the density of products of topological spaces. This theorem was arrived at independently by Hewitt[1], Marczewski[2] and Pondiczery[3] in the 1940s.
Theorem.
Let be an infinite cardinal number and an index set of cardinality at most . If are topological spaces with then
The special case says that the product of at most continuum many separable spaces is separable.
References
- 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 |