Publication: Countable powers of compact Abelian groups in the uniform topology and cardinality of their dual groups
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2014
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Abstract
We equip the product of countably many copies of a compact Abelian group X with the uniform topology, and study some properties of the topological group G thus obtained. In particular, we determine the cardinality of the dual group of G, when X is the circle group: it is precisely 2^c.
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A.V. Arhangel’skii and M.G. Tkachenko, Topological Groups and Related Structures, Atlantis Series in Mathematics, Vol. I, Atlantis Press/World Scientific, Paris–Amsterdam 2008.
H. Anzai and S. Kakutani, Bohr compactifications of a locally compact Abelian group. II. Proc. Imp. Acad. Tokyo 19, (1943). 533–539.
L. Aussenhofer, Contributions to the duality theory of abelian topological groups and to the theory of nuclear groups, Diss. Math. CCCLXXXIV. Warsaw, 1999.
W. Banaszczyk, Additive Subgroups of Topological Vector Spaces. Lecture Notes in Mathematics, 1466. Springer-Verlag, Berlin, 1991.
N. Bourbaki, Elements de mathematique. Premiere partie, Livre III: Topologie Generale. Chapitre X: Espaces Fonctionels.
M. J. Chasco, E. Martín-Peinador and V. Tarieladze, On Mackey Topology for groups, Stud. Math. 132, No.3, 257-284 (1999).
WW. Comfort and Kenneth A. Ross, Pseudocompactness and uniform continuity in topological groups. Pacific J.Math. 16 (1966) 483–496.
D. Dikranjan, E. Mart´ın-Peinador and V. Tarieladze, Group valued null sequences and metrizable non-Mackey groups. Forum Math. Published Online: 2012.02.03.
D. Dikranjan, Iv. Prodanov and L. Stoyanov, Topological Groups: Characters, Dualities and Minimal Group Topologies, Pure and Applied Mathematics, vol. 130, Marcel Dekker Inc., New York-Basel, 1989.
R. Engelking, General topology, Panstwowe Wydawnictwo Naukowe, 1985.
G. Fichtenhollz and L. Kantorovitch, Sur les operations lineaires dans l’espace ses fonctions bornees. Studia Math. 5(1934),69–98.
S.S.Gabriyelyan,Groups of quasi-invariance and the Pontryagin duality.Topology and its Applications, 157 (2010), 2786–2802.
E. Hewitt, and Kenneth A. Ross, Abstract Harmonic Analysis I. Die Grüundlehren der Mathematischen Wissenschaften 115. Springer-Verlag 1963.
S. Kakutani, On cardinal numbers related with a compact Abelian group. Proc. Imp. Acad. Tokyo 19, (1943). 366–372.
J.W. Nienhuys, A solenoidal and monothetic minimally almost periodic group. Fund.Math. 73(1971/72),no.2,167–169.
S. Rolewicz, Some remarks on monothetic groups, Colloq. Math. XIII ( 1964), 28–29.
L. J. Sulley, On countable inductive limits of locally compact abelian groups. J. London Math. Soc.5 (1972), pp. 629–637.
A. Weil, L’integration dans les groupes topologiques et ses applications. (French) Actual. Sci. Ind., no. 869. Hermann et Cie., Paris, 1940. 158 pp
N. Ya. Vilenkin, The theory of characters of topological Abelian groups with boundedness given, Izvestiya Akad. Nauk SSSR. Ser. Mat. 15 (1951), 439–162.