On the extension property of normed spaces over fields with non-archimedean valuations
ジャーナル
フリー
1953 年 5 巻 1 号 p. 1-5
詳細
- Published: 1953 Received: 1952/07/15 Available on J-STAGE: 2006/08/29 Accepted: - Advance online publication: - Revised: -
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訂正情報
訂正日: 2006/08/29 訂正理由: - 訂正箇所: 論文タイトル 訂正内容: Wrong : On the extension property of nonmed spaces over fields with non-archinnedean valuations
Right : On the extension property of nonmed spaces over fields with non-archimedean valuations
訂正日: 2006/08/29 訂正理由: - 訂正箇所: 引用文献情報 訂正内容: Wrong : 1) L. Nachbin, A theorem of the Hahn-Banach type for linear transformations. Trans. Amer. Math. Soc., 68 (1950).
2) E. Artin has introduced the normed space of finite dimension in his lecture 'Algebraic numbers and algebraic functions I.' (1950-1951) Princeton.
3) E. g. the algebraic extension field over a field k, or the totality of continuous mappings of a compact space into k are non-archimedean.
4) We difine a circle of center ξ and radius γ>0 to be a set C={η; η ∈ k, |η-ξ| <γ}.
5) Nachbin has called such a property of the set of circles 'binary intersection property'. cf. l.c. (1).
6) l.c. (2), p. 39.
7) A. W. Ingleton, The Hahn-Banach theorem for non-Archimedean valued fields. Proc. Cambridge Phil. Soc., 48 (1952).
8) A F. Monna, Sur les epaaces linéaires normés, III. Indag. Math., 8 (1946).
9) I. S. Cohen, On non-Archimedean normed spaces. Indag. Math., 10 (1948).
Right : 1) L. Nachbin, A theorem of the Hahn-Banach type for linear transformations. Trans. Amer. Math. Soc., 68 (1950).
2) E. Artin has introduced the normed space of finite dimension in his lecture ‘Algebraic numbers and algebraic functions I.’ (1950-1951) Princeton.
3) E. g. the algebraic extension field over a field k, or the totality of continuous mappings of a compact space into k are non-archimedean.
4) We difine a circle of center ξ and radius γ≥0 to be a set C={η;η∈k,Ιη-ξΙ≤γ}.
5) Nachbin has called such a property of the set of circles ‘binary intersection property’. cf. l. c. (1).
6) l. c. (2), p. 39.
7) A. W. Ingleton, The Hahn-Banach theorem for non-Archimedean valued fields. Proc. Cambridge Phil. Soc., 48 (1952).
8) A. F. Monna, Sur les epaaces linéaires normés, III. Indag. Math., 8 (1946).
9) I. S. Cohen, On non-Archimedean normed spaces. Indag. Math., 10 (1948).
訂正日: 2006/08/29 訂正理由: - 訂正箇所: PDFファイル 訂正内容: -
訂正日: 2006/08/29 訂正理由: - 訂正箇所: 論文タイトル 訂正内容: Wrong : On the extension property of nonmed spaces over fields with non-archimedean valuations
Right : On the extension property of normed spaces over fields with non-archimedean valuations
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