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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
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.

References [Enhancements On Off] (What's this?)

  • [1] G. Bachman, E. Beckenstein, L. Narici and S. Warner, Rings of continuous functions with values in a topological field, Trans. Amer. Math. Soc. 204 (1975), 91-112. MR 0402687 (53:6503)
  • [2] S. Mrówka, Further results on E-compact spaces. I, Acta Math. 120 (1968), 161-185. MR 0226576 (37:2165)

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Keywords: Non-Archimedean valued field, ultraregular space, bornological space, Z-replete space
Article copyright: © Copyright 1978 American Mathematical Society

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