Bornological spaces of non-Archimedean valued functions with the compact-open topology
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- by W. Govaerts PDF
- Proc. Amer. Math. Soc. 78 (1980), 132-134 Request permission
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.References
- George Bachman, Edward Beckenstein, Lawrence Narici, and Seth Warner, Rings of continuous functions with values in a topological field, Trans. Amer. Math. Soc. 204 (1975), 91–112. MR 402687, DOI 10.1090/S0002-9947-1975-0402687-6
- W. Govaerts, Bornological spaces of non-Archimedean valued functions with the point-open topology, Proc. Amer. Math. Soc. 72 (1978), no. 3, 571–575. MR 509257, DOI 10.1090/S0002-9939-1978-0509257-8
- S. Mrówka, Further results on $E$-compact spaces. I, Acta Math. 120 (1968), 161–185. MR 226576, DOI 10.1007/BF02394609
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 132-134
- MSC: Primary 46P05; Secondary 46E10, 54C35
- DOI: https://doi.org/10.1090/S0002-9939-1980-0548100-7
- MathSciNet review: 548100