Geodesic
Compactness in Hom(G, H)
Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 164-170

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

Let G be a locally compact abelian group with Bohr compactification Ga. Then [3, Theorem 1.2] any subset F of G compact in Ga is necessarily compact in G; alternatively, any closed non-compact subset F of G has its closure F– in Ga ≠ F; hence F –\F ≠ ø. One of our aims in the present note is to give a result (Corollary 6) which asserts that F –\F has no points which are Gδs, so that F–\F is a perfect set. Another aim is to give an extension of a cited result of [3] in which commutativity and local compactness are essentially irrelevant, and to unify the proofs. 
Corson, H. H.; Glicksberg, I. Compactness in Hom(G, H). Canadian journal of mathematics, Tome 22 (1970) no. 1, pp. 164-170. doi: 10.4153/CJM-1970-019-1
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[1] 1. Bourbaki, N., Eléments de mathématique. I:Les structures fondamentales de l'analyse. Fasc. VIII. Livre III : Topologie générale. Chapitre 9: Utilisation des nombres réels en topologie générale, 2e éd., Actualités Sci. Indust., No. 1045 (Hermann, Paris, 1958). Google Scholar

[2] 2. Day, M. M., Normed linear spaces (Springer, Berlin, 1958). Google Scholar

[3] 3. Glicksberg, I., Uniform boundedness for groups, Can. J. Math. 14 (1962), 269–276. Google Scholar

[4] 4. Grothendieck, A., Critères de compacité dans les espaces fonctionelles généraux, Amer. J. Math. 74 (1952), 168–186. Google Scholar

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