Geodesic
Non-secular, locally compact TRL groups
Glasgow mathematical journal, Tome 21 (1980) no. 1, pp. 1-7

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

In [12], Loy and Miller proved that a locally compact, eudoxian TR group is algebraically and order-theoretically (and hence, topologically) isomorphic to a finite product of copies of the real numbers. In [18], Wirth used their result to describe the subgroup of a locally compact TR group generated by the compact neighbourhoods of zero. The proof of Loy and Miller relied heavily on a result of Mackey (cf. [10], p. 390) and either the finite-dimensional case of the Choquet-Kendall Theorem (cf. [15], pp. 9–10) or the representation theory of Kakutani (cf. [11], Appendix). Below we use only elementary topological results and order-theoretic arguments and a theorem of Conrad [4] to characterize all non-secular, locally compact TRL groups (Theorem 3). Our proof of Theorem 3 allows us to deduce algebraically the theorems both of Loy and Miller and of Wirth, in both cases without appealing to the theorem of Conrad. 
Redfield, R. H. Non-secular, locally compact TRL groups. Glasgow mathematical journal, Tome 21 (1980) no. 1, pp. 1-7. doi: 10.1017/S0017089500003918
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