阿基米德里兹空间的表示定理

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
A. W. Wickstead
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引用次数: 0

摘要

在以前的著作中,布斯克兹和作者在研究张量积时,利用了阿基米德里兹空间的表示,即定义在拓扑空间密集开放子集上的实值连续函数。这些表示可以通过限制到表示函数为实值而非无限的集合,从小笠原前田表示得到。在本注释中,我们将展示如何通过阶单位空间的柯林-角谷表示简单地得到这种表示。最后,我们将研究这种情况下的里斯兹同态的表示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Representation Theorem for Archimedean Riesz Spaces

In previous works, Buskes and the author have made use of representations of Archimedean Riesz spaces in terms of real-valued continuous functions defined on dense open subsets of a topological space in studying tensor products. These representations may be obtained from the Ogasawara–Maeda representation by means of restriction to the set on which representing functions are real-valued, rather than infinite. In this note, we show how to obtain such a representation as a simple consequence of the Krein–Kakutani representation of an order unit space. We conclude by studying the representation of Riesz homomorphisms in this setting.

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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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