## Factoring functions on Cartesian products

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- by N. Noble and Milton Ulmer
- Trans. Amer. Math. Soc.
**163**(1972), 329-339 - DOI: https://doi.org/10.1090/S0002-9947-1972-0288721-2
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## Abstract:

A function on a product space is said to depend on countably many coordinates if it can be written as a function defined on some countable subproduct composed with the projection onto that subproduct. It is shown, for $X$ a completely regular Hausdorff space having uncountably many nontrivial factors, that each continuous real-valued function on $X$ depends on countably many coordinates if and only if $X$ is pseudo-${\aleph _1}$-compact. It is also shown that a product space is pseudo-${\aleph _1}$-compact if and only if each of its finite subproducts is. (This fact derives from a more general theorem which also shows, for example, that a product satisfies the countable chain condition if and only if each of its finite subproducts does.) All of these results are generalized in various ways.## References

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## Bibliographic Information

- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**163**(1972), 329-339 - MSC: Primary 54.25
- DOI: https://doi.org/10.1090/S0002-9947-1972-0288721-2
- MathSciNet review: 0288721