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Proceedings of the American Mathematical Society

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


Author: W. Govaerts
Journal: Proc. Amer. Math. Soc. 72 (1978), 571-575
MSC: Primary 46P05; Secondary 46E15, 54C40
DOI: https://doi.org/10.1090/S0002-9939-1978-0509257-8
MathSciNet review: 509257
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Abstract: F denotes a nontrivially non-Archimedean valued field with rank one, X an ultraregular space and $ C(X,F,p)$ is the vector space $ C(X,F)$ of all continuous functions from X into F with the topology p of pointwise convergence. We show that $ C(X,F,p)$ is a bornological space if and only if X is a Z-replete space. Also, some results are found concerning the compact-open topology c and we make a comparison with that case as studied by Bachman, Beckenstein, Narici and Warner.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0509257-8
Keywords: Non-Archimedean valued field, ultraregular space, bornological space, Z-replete space
Article copyright: © Copyright 1978 American Mathematical Society