Products of uncountably many $k$-spaces
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- by N. Noble PDF
- Proc. Amer. Math. Soc. 31 (1972), 609-612 Request permission
Abstract:
It is shown that if a product of nonempty spaces is a $k$-space then for each infinite cardinal $\mathfrak {n}$ some product of all but $\mathfrak {n}$ of the factors has each $\mathfrak {n}$-fold subproduct $\mathfrak {n} - {\aleph _0}$-compact (each $\mathfrak {n}$-fold open cover has a finite subcover). An example is given, for each regular $\mathfrak {n}$, of a space $X$ which is not $\mathfrak {n} - {\aleph _0}$-compact (so ${X^{{\mathfrak {n}^ + }}}$ is not a $k$-space) for which ${X^\mathfrak {n}}$ is a $k$-space.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 609-612
- DOI: https://doi.org/10.1090/S0002-9939-1972-0287503-0
- MathSciNet review: 0287503