A constructive treatment of Urysohn's Lemma in an apartness space

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Mathematical Logic Quarterly 52 (5):464-469 (2006)
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Abstract

This paper is dedicated to Prof. Dr. Günter Asser, whose work in founding this journal and maintaining it over many difficult years has been a major contribution to the activities of the mathematical logic community.At first sight it appears highly unlikely that Urysohn's Lemma has any significant constructive content. However, working in the context of an apartness space and using functions whose values are a generalisation of the reals, rather than real numbers, enables us to produce a significant constructive version of that lemma

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10.1002/malq.200610006

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Citations of this work

On the constructive notion of closure maps.Mohammad Ardeshir & Rasoul Ramezanian - 2012 - Mathematical Logic Quarterly 58 (4-5):348-355.
Apartness spaces and uniform neighbourhood structures.Douglas S. Bridges - 2016 - Annals of Pure and Applied Logic 167 (9):850-864.

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Apartness spaces as a framework for constructive topology.Douglas Bridges & Luminiţa Vîţă - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.
Apartness spaces as a framework for constructive topology.Douglas Bridges & Luminia Vî - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.

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