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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The class of compact* spaces is productive and closed hereditary


Author: W. Govaerts
Journal: Proc. Amer. Math. Soc. 66 (1977), 167-168
MSC: Primary 54D30
MathSciNet review: 0461432
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0461432-6
Keywords: Compact$ ^ \ast $ spaces, E-compactness, ring of continuous functions, representation of homomorphisms
Article copyright: © Copyright 1977 American Mathematical Society