Dimension, Linear Functionals, and Norms in a Vector Space

被引：0

作者：

Kwon, Miyeon ^{[1
]}

机构：

[1] Univ Wisconsin Platteville, Dept Math, Platteville, WI 53818 USA

来源：

AMERICAN MATHEMATICAL MONTHLY | 2010年 / 117卷 / 08期

关键词：

D O I：

10.4169/000298910X515811

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the axiom of choice, we prove a generalized converse of the well-known fact that if X is a finite-dimensional vector space, then any linear functional on X is continuous with respect to all norms defined on X. We also show that an infinite-dimensional real or complex vector space X has exactly 2(dim(x)) inequivalent norms.

引用

页码：738 / 740

页数：3

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