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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on $ C\sb{c}(X)$


Authors: G. D. Richardson and D. C. Kent
Journal: Proc. Amer. Math. Soc. 49 (1975), 441-445
MSC: Primary 54C35; Secondary 54A20
MathSciNet review: 0370483
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Abstract: When $ X$ is a locally convex topological linear space, the function algebra $ {C_c}(X)$ (with continuous convergence) can have a closure operator which has infinitely many distinct iterations. The reverse situation is also possible: $ X$ can be a locally compact $ c$-embedded convergence space whose closure operator has infinitely many distinct iterations, whereas $ {C_c}(X)$ is a topological space.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0370483-X
PII: S 0002-9939(1975)0370483-X
Keywords: Convergence space, continuous convergence, $ c$-embedded space, highly nontopological space
Article copyright: © Copyright 1975 American Mathematical Society