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

 

Bornological spaces of non-Archimedean valued functions with the compact-open topology


Author: W. Govaerts
Journal: Proc. Amer. Math. Soc. 78 (1980), 132-134
MSC: Primary 46P05; Secondary 46E10, 54C35
MathSciNet review: 548100
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Abstract: Let F be a field with nontrivial non-Archimedean valuation of rank one and let X be a zero-dimensional Hausdorff space. The vector space $ C(X,F)$ of all continuous functions from X into F is provided with the compact-open topology c. We prove that $ C(X,F,c)$ is bornological if and only if X is a Z-replete space.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0548100-7
PII: S 0002-9939(1980)0548100-7
Keywords: Non-Archimedean valued field, ultraregular space, bornological space, compact-open topology, Z-replete space
Article copyright: © Copyright 1980 American Mathematical Society