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Hewitt-Marczewski-Pondiczery theorem
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(Theorem)
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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 $\kappa$ be an infinite cardinal number and $S$ an index set of cardinality at most $2^\kappa$ . If $X_s$ $(s\in S)$ are topological spaces with $d(X_s)\le\kappa$ then$$ d\left(\prod_{s\in S}X_s\right)\le\kappa.$$
The special case $\kappa=\aleph_0$ says that the product of at most continuum many separable spaces is separable.
- 1
- Edwin Hewitt, A remark on density characters, Bull. Amer. Math. Soc. 52 (1946), 641-643.
- 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 Virtual Library of Science: Fundamenta Mathematicae, Volume 34.)
- 3
- E. S. Pondiczery, Power problems in abstract spaces, Duke Math. J. 11 (1944), 835-837.
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"Hewitt-Marczewski-Pondiczery theorem" is owned by yark.
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Cross-references: separable, separable spaces, continuum many, cardinality, index set, cardinal number, infinite, topological spaces, products, density
There is 1 reference to this entry.
This is version 2 of Hewitt-Marczewski-Pondiczery theorem, born on 2007-06-19, modified 2007-06-19.
Object id is 9623, canonical name is HewittMarczewskiPondiczeryTheorem.
Accessed 1038 times total.
Classification:
| AMS MSC: | 54A25 (General topology :: Generalities :: Cardinality properties ) | | | 54D65 (General topology :: Fairly general properties :: Separability) |
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Pending Errata and Addenda
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