PSEUDOCONTINUITY IS NECESSARY AND SUFFICIENT FOR ORDER-PRESERVING CONTINUOUS REPRESENTATIONS

Vincenzo Scalzo

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PSEUDOCONTINUITY IS NECESSARY AND SUFFICIENT FOR ORDER-PRESERVING CONTINUOUS REPRESENTATIONS

机译：伪连续性对于保留顺序的连续表示是必要且充分的

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Using some properties of pseudocontinuous functions - a recent generalization of continuous functions - and without invoking Debreu's Open Gap Theorem, we solve the following problem: given a pseudocontinuous function v, find a continuous function u such that u(x) > u(y) if and only if v(x) > v(y). We show that this problem can be solved only for pseudocontinuous functions. Finally, we obtain a new proof on the existence of continuous numerical representations for continuous, transitive and total binary relations.

机译：使用伪连续函数的某些属性-连续函数的最新泛化-并且不调用Debreu的开放间隙定理，我们解决了以下问题：给定伪连续函数v，找到一个连续函数u使得u（x）> u（y）当且仅当v（x）> v（y）。我们表明，仅伪连续函数可以解决此问题。最后，我们获得了关于连续，传递和总二元关系的连续数值表示形式的新证明。

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来源
《Real analysis exchange》 |2009年第1期|239-248|共10页
作者
Vincenzo Scalzo;
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作者单位

Dipartimento di Matematica e Statistica. Universita di Napoli Federico II, via Cinthia (Monte S. Angelo), 80126 Napoli, Italy;

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原文格式 PDF
正文语种 eng
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关键词
pseudocontinuous functions; order-preserving functions; continuous numerical representations of binary relations;

机译：伪连续函数;保持订单的功能;二元关系的连续数值表示;

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PSEUDOCONTINUITY IS NECESSARY AND SUFFICIENT FOR ORDER-PRESERVING CONTINUOUS REPRESENTATIONS

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