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Mat. Sb., 2003, Volume 194, Number 10, Pages 3–26 (Mi msb771)  

This article is cited in 1 scientific paper (total in 1 paper)

Two classes of spaces reflexive in the sense of Pontryagin

S. S. Akbarova, E. T. Shavgulidzeb

a All-Russian Institute for Scientific and Technical Information of Russian Academy of Sciences
b M. V. Lomonosov Moscow State University

Abstract: The Pontryagin–van Kampen duality for locally compact Abelian groups can be generalized in two ways to wider classes of topological Abelian groups: in the first approach the dual group $X^\bullet$ is endowed with the topology of uniform convergence on compact subsets of $X$ and in the second, with the topology of uniform convergence on totally bounded subsets of $X$. The corresponding two classes of groups “reflexive in the sense of Pontryagin–van Kampen” are very wide and are so close to each other that it was unclear until recently whether they coincide or not. A series of counterexamples constructed in this paper shows that these classes do not coincide and also answer several other questions arising in this theory. The results of the paper can be interpreted as evidence that the second approach to the generalization of the Pontryagin duality is more natural.

DOI: https://doi.org/10.4213/sm771

Full text: PDF file (390 kB)
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English version:
Sbornik: Mathematics, 2003, 194:10, 1427–1449

Bibliographic databases:

UDC: 519.4+513.88
MSC: Primary 22A05, 54H11; Secondary 46A03
Received: 09.01.2003

Citation: S. S. Akbarov, E. T. Shavgulidze, “Two classes of spaces reflexive in the sense of Pontryagin”, Mat. Sb., 194:10 (2003), 3–26; Sb. Math., 194:10 (2003), 1427–1449

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. M.J. Chasco, D. Dikranjan, E. Martín-Peinador, “A survey on reflexivity of abelian topological groups”, Topology and its Applications, 159:9 (2012), 2290  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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