Serviços Personalizados
Journal
Artigo
Indicadores
- Citado por SciELO
- Acessos
Links relacionados
- Citado por Google
- Similares em SciELO
- Similares em Google
Compartilhar
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
1 Universidad Nacional de Colombia, Bogotá, Colombia
2 Universidad Industrial de Santander, Bucaramanga, Colombia
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
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
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
[1] N. Bourbaki, Elements of Mathematics. General topology (part 1), Addison-Wesley Publishing Company, Massachusetts, 1966. [ Links ]
[2] H. Herrlich, Axiom of choice, Lecture Notes in Mathematics, vol. 1876, Springer-Verlag, Berlin, 2006. [ Links ]
[3] R. Lubarsky, On the Cauchy completeness of the constructive Cauchy reals, Math. Log. Q. 53 (2007), 396-414. [ Links ]
[4] R. Lubarsky and M. Rathjen, On the constructive Dedekind reals, Logic and Analysis (2008), 131-152. [ Links ]
[5] R. Lubarsky and F. Richman, Signed-bit representations of real numbers, J. Log. Anal. (2009), 1-18. [ Links ]
[6] F. Richman, The fundamental theorem of algebra: a constructive development without choice, Pacific J. Math. 196 (2000), no. 1, 213-230. [ Links ]
[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