Completion of premetric spaces

José Andrés Quintero; Carlos Enrique Uzcátegui

doi:10.15446/recolma.v54n1.89776

Published

2020-01-01

Completion of premetric spaces

Completación de espacios premétricos

DOI:

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

Keywords:

Completion, premetrics space, regular families, Cauchy families, constructive mathematics (en)
Completación, espacios premétricos, familias regulares, familias de Cauchy, matemáticas constructivas (es)

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Authors

José Andrés Quintero Universidad Nacional de Colombia
Carlos Enrique Uzcátegui Universidad Industrial de Santander

Abstract (en)
Abstract (es)

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.

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

References

N. Bourbaki, Elements of Mathematics. General topology (part 1), Addison-Wesley Publishing Company, Massachusetts, 1966.

H. Herrlich, Axiom of choice, Lecture Notes in Mathematics, vol. 1876, Springer-Verlag, Berlin, 2006.

R. Lubarsky, On the Cauchy completeness of the constructive Cauchy reals, Math. Log. Q. 53 (2007), 396-414.

R. Lubarsky and M. Rathjen, On the constructive Dedekind reals, Logic and Analysis (2008), 131-152.

R. Lubarsky and F. Richman, Signed-bit representations of real numbers, J. Log. Anal. (2009), 1-18.

F. Richman, The fundamental theorem of algebra: a constructive development without choice, Pacific J. Math. 196 (2000), no. 1, 213-230.

F. Richman, 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

F. Richman, Real numbers and other completions, Math. Log. Q. 54 (2008), no. 1, 98-108.

A. Setzer, Mr2387400, Math. Log. Quart.

S. Willard, General Topology, Dover Publications, INC, Mineola, 2004.

How to Cite

APA

Quintero, J. A. and Uzcátegui, C. E. (2020). Completion of premetric spaces. Revista Colombiana de Matemáticas, 54(1), 19–29. https://doi.org/10.15446/recolma.v54n1.89776

ACM

[1]

Quintero, J.A. and Uzcátegui, C.E. 2020. Completion of premetric spaces. Revista Colombiana de Matemáticas. 54, 1 (Jan. 2020), 19–29. DOI:https://doi.org/10.15446/recolma.v54n1.89776.

ACS

(1)

Quintero, J. A.; Uzcátegui, C. E. Completion of premetric spaces. rev.colomb.mat 2020, 54, 19-29.

ABNT

QUINTERO, J. A.; UZCÁTEGUI, C. E. Completion of premetric spaces. Revista Colombiana de Matemáticas, [S. l.], v. 54, n. 1, p. 19–29, 2020. DOI: 10.15446/recolma.v54n1.89776. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/89776. Acesso em: 22 jan. 2025.

Chicago

Quintero, José Andrés, and Carlos Enrique Uzcátegui. 2020. “Completion of premetric spaces”. Revista Colombiana De Matemáticas 54 (1):19-29. https://doi.org/10.15446/recolma.v54n1.89776.

Harvard

Quintero, J. A. and Uzcátegui, C. E. (2020) “Completion of premetric spaces”, Revista Colombiana de Matemáticas, 54(1), pp. 19–29. doi: 10.15446/recolma.v54n1.89776.

IEEE

[1]

J. A. Quintero and C. E. Uzcátegui, “Completion of premetric spaces”, rev.colomb.mat, vol. 54, no. 1, pp. 19–29, Jan. 2020.

MLA

Quintero, J. A., and C. E. Uzcátegui. “Completion of premetric spaces”. Revista Colombiana de Matemáticas, vol. 54, no. 1, Jan. 2020, pp. 19-29, doi:10.15446/recolma.v54n1.89776.

Turabian

Quintero, José Andrés, and Carlos Enrique Uzcátegui. “Completion of premetric spaces”. Revista Colombiana de Matemáticas 54, no. 1 (January 1, 2020): 19–29. Accessed January 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/89776.

Vancouver

1.

Quintero JA, Uzcátegui CE. Completion of premetric spaces. rev.colomb.mat [Internet]. 2020 Jan. 1 [cited 2025 Jan. 22];54(1):19-2. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/89776