Hewitt-Marczewski-Pondiczery theorem
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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: Bull. 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: Fundamenta Mathematicae, Volume 34.)
- 3 E. S. Pondiczery, Power problems in abstract spaces, Duke Math. J. 11 (1944), 835–837.
Type of Math Object:
Theorem
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Reference
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Mathematics Subject Classification
54D65 Separability54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
