Duality properties of spaces of non-Archimedean valued functions

Journal of the Australian Mathematical Society

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