The class of compact* spaces is productive and closed hereditary
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- by W. Govaerts PDF
- Proc. Amer. Math. Soc. 66 (1977), 167-168 Request permission
Abstract:
W. W. Comfort defined compact$^ \ast$ spaces as completely regular Hausdorff spaces X such that each maximal ideal in the ring ${C^ \ast }(X,{\mathbf {R}})$ of bounded continuous real-valued functions on X is fixed. He showed that, independently of the axiom of choice, the class of compact$^ \ast$ spaces is productive and closed hereditary. We give a short new proof of this.References
- W. W. Comfort, A theorem of Stone-Čech type, and a theorem of Tychonoff type, without the axiom of choice; and their realcompact analogues, Fund. Math. 63 (1968), 97–110. MR 236880, DOI 10.4064/fm-63-1-97-110
- W. Govaerts, Representation and determination problems: a case study, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), no. 1, 57–59 (English, with Russian summary). MR 402675
- W. Govaerts, A separation axiom for the study of function space structures, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), no. 1, 65–69 (English, with Russian summary). MR 402676
- Sergio Salbany, On compact$^{\ast }$ spaces and compactifications, Proc. Amer. Math. Soc. 45 (1974), 274–280. MR 355970, DOI 10.1090/S0002-9939-1974-0355970-1
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 66 (1977), 167-168
- MSC: Primary 54D30
- DOI: https://doi.org/10.1090/S0002-9939-1977-0461432-6
- MathSciNet review: 0461432