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The Kripke schema in metric topology

被引：3
|
作者：
Lubarsky, Robert [2 ]
Richman, Fred [2 ]
Schuster, Peter [1 ]
机构：
[1] Univ Leeds, Leeds LS2 9JT, W Yorkshire, England
[2] Florida Atlantic Univ, Dept Math Sci, Boca Raton, FL 33431 USA
来源：
MATHEMATICAL LOGIC QUARTERLY | 2012年 / 58卷 / 06期
关键词：
Constructive reverse mathematics; Countable; Kripke schema; Metric space; Separable;
D O I：
10.1002/malq.201200018
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A form of Kripke's schema turns out to be equivalent to each of the following two statements from metric topology: every open subspace of a separable metric space is separable; every open subset of a separable metric space is a countable union of open balls. Thus Kripke's schema serves as a point of reference for classifying theorems of classical mathematics within Bishop-style constructive reverse mathematics. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
引用
收藏
页码：498 / 501
页数：4
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