A note on embedding subgroups of products topological groups

Margarita Gary Gutiérrez,; Constancio Hernández García; Adolfo Pimienta Acosta

Margarita Gary Gutiérrez, Universidad del Atlántico Puerto Colombia-Colombia.
Constancio Hernández García Universidad Autónoma Metropolitana
Adolfo Pimienta Acosta Universidad Simón Bolívar

Keywords: Topological group, topological group $\omega$-narrow, topological group $\omega$-balanced and topological isomorphism. Grupos topol\'ogicos, grupos topol\'ogicos $\omega$-estrechos, grupos topol\'ogicos $\omega$-balacenados e isomorfismos topol\'ogicos.

Abstract

In this paper, we study $\omega$-narrow and $\omega$-balanced topological groups and prove they may be embedded as subgroups of products of second countable (resp, first countable) topological groups. We also prove that this kind of groups are closed with respect to the most common operations, such as the taking of subgroups, arbitrary products and under continuos homomorphic images. We finally prove that the class of $\omega$-balanced topological groups is wider than the class of $\omega$-narrow topological groups.

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Author Biographies

Constancio Hernández García, Universidad Autónoma Metropolitana

Departamento de Matemáticas,Universidad Autónoma Metropolitana, prolongaci\'on canal de miramontes $\# $3855, Col. Ex-Hacienda San Juan de Dios, Delegaci\'on Tlalpan, C.P. 14387, M\'exico, D.F-M\'exico.\\

Adolfo Pimienta Acosta, Universidad Simón Bolívar

Facultad de Ciencias B\'asicas y Biom\'edicas, Universidad Sim\'on Bolivar, Barranquilla, Colombia

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