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The Kripke schema in metric topology
Authors:Robert Lubarsky  Fred Richman  Peter Schuster
Institution:1. Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, United States of America;2. Pure Mathematics, University of Leeds, Leeds LS2 9JT, England
Abstract: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.
Keywords:Kripke schema  constructive reverse mathematics  metric space  countable  separable  MSC (2010) 03B30  03F55  03F60  54E35
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