Journal of the Australian Mathematical Society | |
Duality properties of spaces of non-Archimedean valued functions | |
W. Govaerts1  | |
关键词: 46 P 05; | |
DOI : 10.1017/S1446788700033942 | |
学科分类:数学(综合) | |
来源: Cambridge University Press | |
【 摘 要 】
Let C(X, F) be the space of all continuous functions from the ultraregular compact Hausdorff space X into the separated locally K-convex space F; K is a complete, but not necessarily spherically complete, non-Archimedean valued field and C(X, F) is provided with the topology of uniform convergence on X We prove that C(X, F) is K-barrelled (respectively K-quasibarrelled) if and only if F is K-barrelled (respectively K-quasibarrelled) This is not true in the case of R or C-valued functions. No complete characterization of the K-bornological space C(X, F) is obtained, but our results are, nevertheless, slightly better than the Archimedean ones. Finally, we introduce a notion of K-ultrabornological spaces for K non-spherically complete and use it to study K-ultrabornological spaces C(X, F).
【 授权许可】
Unknown
【 预 览 】
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