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Revista Colombiana de Matemáticas

versão impressa ISSN 0034-7426

Rev.colomb.mat. vol.54 no.1 Bogotá jan./jun. 2020

https://doi.org/10.15446/recolma.v54n1.89776 

Original articles

Completion of premetric spaces

Completación de espacios premétricos

José Andrés Quintero1  * 

Carlos Enrique Uzcátegui2 

1 Universidad Nacional de Colombia, Bogotá, Colombia

2 Universidad Industrial de Santander, Bucaramanga, Colombia


Abstract:

We study the concept of a premetric space introduced by F. Richman in the context of constructive mathematics, and present a method for completing them.

Keywords: Completion; premetrics space; regular families; Cauchy families; constructive mathematics

Resumen:

Estudiamos el concepto de espacio premétrico introducido por F. Richman en el contexto de las matemáticas constructivas, y presentamos un método para completarlos.

Palabras clave: Completación; espacios premétricos; familias regulares; familias de Cauchy; matemáticas constructivas

Full text available only in PDF format.

Acknowledgment.

The authors wish to thank the referee for his (her) comments which improved the presentation of the results. The second author thanks la Vicerrectoría de Investigación y Extensión de la Universidad Industrial de Santander for the financial support for this work, which is part of the VIE project #2422.

REFERENCES

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[7] ______, Constructive mathematics without choice, Reuniting the antipodes-constructive and nonstandard views of the continuum (Venice, 1999), Synthese Lib., vol. 306, Kluwer Acad. Publ., Dordrecht, 2001, pp. 199-205. MR 1895394 [ Links ]

[8] ______, Real numbers and other completions, Math. Log. Q. 54 (2008), no. 1, 98-108. [ Links ]

[9] A. Setzer, Mr2387400, Math. Log. Quart. [ Links ]

[10] S. Willard, General Topology, Dover Publications, INC, Mineola, 2004. [ Links ]

Received: August 16, 2019; Accepted: October 16, 2019

*Correspondencia: José Andrés Quintero, Departamento de Matemáticas, Universidad Nacional de Colombia, Facultad de Ciencias, Carrera 30, calle 45, Bogotá, Colombia. Correo electrónico: joquinteroc@unal.edu.co. DOI: https://doi.org/10.15446/recolma.v54n1.89776

2010 Mathematics Subject Classification. 53C21, 53C42.

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License