# Strong reflexivity of Abelian groups

Montserrat Bruguera; María Jesús Chasco

Czechoslovak Mathematical Journal (2001)

- Volume: 51, Issue: 1, page 213-224
- ISSN: 0011-4642

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topBruguera, Montserrat, and Chasco, María Jesús. "Strong reflexivity of Abelian groups." Czechoslovak Mathematical Journal 51.1 (2001): 213-224. <http://eudml.org/doc/30629>.

@article{Bruguera2001,

abstract = {A reflexive topological group $G$ is called strongly reflexive if each closed subgroup and each Hausdorff quotient of the group $G$ and of its dual group is reflexive. In this paper we establish an adequate concept of strong reflexivity for convergence groups. We prove that complete metrizable nuclear groups and products of countably many locally compact topological groups are BB-strongly reflexive.},

author = {Bruguera, Montserrat, Chasco, María Jesús},

journal = {Czechoslovak Mathematical Journal},

keywords = {Pontryagin duality theorem; dual group; convergence group; continuous convergence; reflexive group; strong reflexive group; k-space; Čech complete group; k-group; Pontryagin duality theorem; dual group; convergence group; continuous convergence; reflexive group; k-space; Čech complete group},

language = {eng},

number = {1},

pages = {213-224},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Strong reflexivity of Abelian groups},

url = {http://eudml.org/doc/30629},

volume = {51},

year = {2001},

}

TY - JOUR

AU - Bruguera, Montserrat

AU - Chasco, María Jesús

TI - Strong reflexivity of Abelian groups

JO - Czechoslovak Mathematical Journal

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 51

IS - 1

SP - 213

EP - 224

AB - A reflexive topological group $G$ is called strongly reflexive if each closed subgroup and each Hausdorff quotient of the group $G$ and of its dual group is reflexive. In this paper we establish an adequate concept of strong reflexivity for convergence groups. We prove that complete metrizable nuclear groups and products of countably many locally compact topological groups are BB-strongly reflexive.

LA - eng

KW - Pontryagin duality theorem; dual group; convergence group; continuous convergence; reflexive group; strong reflexive group; k-space; Čech complete group; k-group; Pontryagin duality theorem; dual group; convergence group; continuous convergence; reflexive group; k-space; Čech complete group

UR - http://eudml.org/doc/30629

ER -

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