Continuous Order-Preserving Functions for All Kind of Preorders

Gianni Bosi

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Continuous Order-Preserving Functions for All Kind of Preorders

机译：Continuous Order-Preserving Functions for All Kind of Preorders

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A topology is said to be strongly useful if every weakly continuous preorder admits a continuous order-preserving function. A strongly useful topology is useful, in the sense that every continuous total preorder admits a continuous utility representation. In this paper, I study the structure of strongly useful topologies. The existence of a natural one-to-one correspondence is proved, between weakly continuous preorders and equivalence classes of families of complete separable systems. In some sense, this result completely clarifies the connections between order theory and topology. Then, I characterize strongly useful topologies and I present a property concerning subspace topologies of strongly useful topo-logical spaces.

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来源
《Order: A Journal on the theory of ordered sets》 |2023年第1期|87-97|共11页
作者
Gianni Bosi;
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作者单位

DEAMS, University of Trieste, Via Valerio 1, 34127 Trieste, Italy;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种英语
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关键词
Useful topology; Complete separable system; Weak topology; Completely regular space; Normal space; Strongly useful topology;

Continuous Order-Preserving Functions for All Kind of Preorders

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