Strong reflexivity of Abelian groups

Montserrat Bruguera; María Jesús Chasco

Czechoslovak Mathematical Journal (2001)

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

Abstract

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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.

How to cite

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Bruguera, 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 -

References

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  1. Additive Subgroups of Topological Vector Spaces. Lecture Notes in Mathematics 1466, Springer-Verlag, Berlin-Heidelberg-New York, 1991. (1991) MR1119302
  2. Continuous Convergence in C ( X ) . Lecture Notes in Mathematics 469, Springer-Verlag, Berlin-Heidelberg-New York, 1975. (1975) MR0461418
  3. 10.1017/S0305004100051483, Math. Proc. Camb. Phil. Soc. 78 (1975), 19–32. (1975) MR0453915DOI10.1017/S0305004100051483
  4. Pontryagin duality for convergence groups of unimodular continuous functions, Czechoslovak Math. J. 33 (1983), 212–220. (1983) Zbl0528.54005MR0699022
  5. c -Duality Theory for Convergence Groups. Lecture in the Course “Convergence and Topology”, Erice, 1998. (1998) 
  6. 10.1007/s000130050160, Arch. Math. 70 (1998), 22–28. (1998) Zbl0899.22001MR1487450DOI10.1007/s000130050160
  7. 10.1007/BF01189829, Arch. Math. 63 (1994), 264–270. (1994) MR1287256DOI10.1007/BF01189829
  8. 10.1007/BF01360283, Math. Ann. 159 (1965), 94–104. (1965) MR0179752DOI10.1007/BF01360283
  9. Limesräume, Math. Ann. 137 (1959), 269–303. (1959) Zbl0086.08803MR0109339
  10. Extensions of the Pontryagin duality I: Infinite products, B. G. Duke Math. 15 (1948), 649–658. (1948) MR0026999
  11. Bemerkung zu einem Satz von S. Kaplan, B. G.  Arch. der Math. 6 (1955), 264–268. (1955) Zbl0065.01601MR0066397
  12. 10.2307/2161108, Proc. Amer. Math. Soc. 123 (1995), 3563–3566. (1995) MR1301516DOI10.2307/2161108
  13. K -groups and duality, Trans. Amer. Math. Soc. 151 (1970), 551–561. (1970) Zbl0229.22012MR0270070
  14. Uniform Structures on Topological Groups and Their Quotients. Advanced Book Program, McGraw-Hill International Book Company, 1981. (1981) MR0644485

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