Completion of premetric spaces

José Andrés Quintero; Carlos Enrique Uzcátegui

doi:10.15446/recolma.v54n1.89776

Publié-e

2020-01-01

Completion of premetric spaces

Completación de espacios premétricos

DOI :

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

Mots-clés :

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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Auteurs-es

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

Résumé (en)
Résumé (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.

Références

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.

Comment citer

APA

Quintero, J. A. et 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. et Uzcátegui, C.E. 2020. Completion of premetric spaces. Revista Colombiana de Matemáticas. 54, 1 (janv. 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 janv. 2025.

Chicago

Quintero, José Andrés, et 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. et Uzcátegui, C. E. (2020) « Completion of premetric spaces », Revista Colombiana de Matemáticas, 54(1), p. 19–29. doi: 10.15446/recolma.v54n1.89776.

IEEE

[1]

J. A. Quintero et C. E. Uzcátegui, « Completion of premetric spaces », rev.colomb.mat, vol. 54, nᵒ 1, p. 19–29, janv. 2020.

MLA

Quintero, J. A., et C. E. Uzcátegui. « Completion of premetric spaces ». Revista Colombiana de Matemáticas, vol. 54, nᵒ 1, janvier 2020, p. 19-29, doi:10.15446/recolma.v54n1.89776.

Turabian

Quintero, José Andrés, et Carlos Enrique Uzcátegui. « Completion of premetric spaces ». Revista Colombiana de Matemáticas 54, no. 1 (janvier 1, 2020): 19–29. Consulté le janvier 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]. 1 janv. 2020 [cité 22 janv. 2025];54(1):19-2. Disponible à: https://revistas.unal.edu.co/index.php/recolma/article/view/89776