Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
Tychonoff and connected products theorems are equivalent
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Keywords

compactness
connectedness
choice axiom
compacidad
conexidad
axioma de elección

How to Cite

Pérez, J. A. (2017). Tychonoff and connected products theorems are equivalent. Revista De Matemática: Teoría Y Aplicaciones, 23(1), 1–10. https://doi.org/10.15517/rmta.v23i1.22336

Abstract

In Topology, Tychonoff’s theorem asserts that the compactness of a product of topological spaces and compactness of each of its factors are equivalent facts. Analogously, the connected products theorem does the same about connectedness. This note is devoted to prove the equivalence between thes two topological results.

https://doi.org/10.15517/rmta.v23i1.22336
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References

García Máynez, A. (2011) Introducción a la Topología de Conjuntos. Aportaciones Matemáticas No. 36, Sociedad Matemática Mexicana, México D.F.

Kelley, J.L. (1950) “The Tychonoff product theorem implies the axiom of choice”, Fundamenta Mathematica 37: 75–76.

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Pérez, J.A. (2015) Topología de Conjuntos, un Primer Curso. Publicaciones Electrónicas, Vol. 18, Sociedad Matemática Mexicana, México D.F. http://sociedadmatematicamexicana.org.mx/SEPA/ECMS/resumen/P1TE19_1.pdf

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Tychonoff, A.N. (1929) “Über die topologische Erweiterung von Räumen”, Mathematische Annalen 102: 544–561.

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