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

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

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
Keywords Urysohn's Lemma  apartness spaces  Constructive mathematics
Categories (categorize this paper)
DOI 10.1002/malq.200610006
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 38,928
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

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.

Add more references

Citations of this work BETA

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.

Add more citations

Similar books and articles

Compactness Notions for an Apartness Space.Douglas S. Bridges - 2012 - Archive for Mathematical Logic 51 (5-6):517-534.
Effective Borel Degrees of Some Topological Functions.Guido Gherardi - 2006 - Mathematical Logic Quarterly 52 (6):625-642.
Product a-Frames and Proximity.Douglas S. Bridges - 2008 - Mathematical Logic Quarterly 54 (1):12-26.
Generalising Compactness.Hannes Diener - 2008 - Mathematical Logic Quarterly 54 (1):49-57.
Apartness Spaces as a Framework for Constructive Topology.Douglas Bridges & Luminiţa Vîţă - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.
Decision Procedure of Some Relevant Logics: A Constructive Perspective.Jacques Riche - 2005 - Journal of Applied Non-Classical Logics 15 (1):9-23.
Weak König's Lemma Implies Brouwer's Fan Theorem: A Direct Proof.Hajime Ishihara - 2006 - Notre Dame Journal of Formal Logic 47 (2):249-252.

Analytics

Added to PP index
2013-12-01

Total views
8 ( #698,519 of 2,319,040 )

Recent downloads (6 months)
4 ( #326,419 of 2,319,040 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature