A note on pseudocompact spaces and $k_{R}$-spaces
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- by Akio Kato PDF
- Proc. Amer. Math. Soc. 63 (1977), 175-176 Request permission
Abstract:
Utilizing the Stone-Čech compactification of an uncountable discrete space, we construct a pseudocompact space X which belongs to Frolík’s class ${\mathfrak {P}^ \ast }$ but ${k_R}X$ is not pseudocompact.References
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J. L. Blasco, An example of a space X in ${\mathfrak {P}^ \ast }$ for which ${k_R}X$ is not pseudocompact, Collect. Math. (to appear).
- Zdeněk Frolík, The topological product of two pseudocompact spaces, Czechoslovak Math. J. 10(85) (1960), 339–349 (English, with Russian summary). MR 116304, DOI 10.21136/CMJ.1960.100418
- Norman Noble, Countably compact and pseudo-compact products, Czechoslovak Math. J. 19(94) (1969), 390–397. MR 248717, DOI 10.21136/CMJ.1969.100911
- N. Noble, The continuity of functions on Cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187–198. MR 257987, DOI 10.1090/S0002-9947-1970-0257987-5
- Russell C. Walker, The Stone-Čech compactification, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 83, Springer-Verlag, New York-Berlin, 1974. MR 0380698, DOI 10.1007/978-3-642-61935-9
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 63 (1977), 175-176
- MSC: Primary 54D30; Secondary 54G20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0433384-6
- MathSciNet review: 0433384