A DICHOTOMY THEOREM FOR THE ELLENTUCK TOPOLOGY

Andrzej Nowik; Patrick Reardon

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A DICHOTOMY THEOREM FOR THE ELLENTUCK TOPOLOGY

机译：ELLENTUCK拓扑的二分法定理

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摘要

Results are deduced from the following dichotomy which reduces descriptive properties concerning the Ellentuck topology to two well-known examples. Theorem: Every nonempty perfect set in the Ellentuck topology contains a closed copy of the Sorgenfrey line or a closed copy of the rational numbers. This leads to a Marczewski-Burstin representation for Marczewski sets in the Ellentuck topology.

机译：从以下二分法得出结果，该二分法将与Ellentuck拓扑有关的描述性降低为两个众所周知的示例。定理：Ellentuck拓扑中的每个非空完美集都包含Sorgenfrey线的封闭副本或有理数的封闭副本。这导致Ellentuck拓扑中Marczewski集的Marczewski-Burstin表示。

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来源
《Real analysis exchange》 |2004年第2期|p.531-542|共12页
作者
Andrzej Nowik; Patrick Reardon;
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作者单位

Department of Mathematics, Gdansk University, Wita Stwosza 57, 80-952 Gdansk, Poland;

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原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
ellentuck topology; exponential space; marczewski set; marczewski-burstin representation;

机译：埃伦塔克拓扑;指数空间;Marczewski集;Marczewski-Burstin表示;

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A DICHOTOMY THEOREM FOR THE ELLENTUCK TOPOLOGY

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