Geodesic
A note on the duality of locally compact groups
Glasgow mathematical journal, Tome 9 (1968) no. 2, pp. 87-91

Voir la notice de l'article provenant de la source Cambridge University Press

Let H be a group of characters on an (algebraic) abelian group G. In a natural way, we may regard G as a group of characters on H. In this way, we obtain a duality between the two groups G and H. One may pose several problems about this duality. Firstly, one may ask whether there exists a group topology on G for which H is precisely the set of continuous characters. This question has been answered in the affirmative in [1]. We shall say that such a topology is compatible with the duality between G and H. Next, one may ask whether there exists a locally compact group topology on G which is compatible with a given duality and, if so, whether there is more than one such topology. It is this second question (previously considered by other authors, to whom we shall refer below) which we shall consider here. 
Baker, J. W. A note on the duality of locally compact groups. Glasgow mathematical journal, Tome 9 (1968) no. 2, pp. 87-91. doi: 10.1017/S0017089500000343
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[1] 1.Varopoulos, N. Th., Studies in harmonic analysis, Proc. Camb. Philos. Soc. 60 (1964), 465–516. Google Scholar | DOI

[2] 2.Glicksberg, I., Uniform boundedness for groups, Canad. J. Math. 14 (1962), 269–276. Google Scholar | DOI

[3] 3.Komura, Y., Some examples on linear topological spaces, Math. Ann. 153 (1964), 150–162. Google Scholar | DOI

[4] 4.Husain, T., Semi-topological groups and linear spaces, Math. Ann. 160 (1965), 146–160. Google Scholar | DOI

[5] 5.Husain, T., Introduction to topological groups (Philadelphia and London, 1966). Google Scholar

[6] 6.Hewitt, E., A remark on characters of locally compact abelian groups, Fund. Math. 53 (1964), 55–64. Google Scholar | DOI

[7] 7.Ross, K. A., Closed subgroups of locally compact abelian groups, Fund. Math. 56 (1965), 241–243. Google Scholar | DOI

[8] 8.Rickert, N. W., Locally compact topologies for groups, Trans. Amer. Math. Soc. 126 (1967), 225–235. Google Scholar | DOI

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