Geodesic
On the Group of Isometries on a Locally Compact Metric Space
Journal of Lie theory, Tome 13 (2003) no. 1, pp. 7-12
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We study conditions under which the group of isometries on a locally compact metric space is locally compact, or acts properly. 
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     author = {A. Manoussos and P. Strantzalos},
     title = {On the {Group} of {Isometries} on a {Locally} {Compact} {Metric} {Space}},
     journal = {Journal of Lie theory},
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A. Manoussos; P. Strantzalos. On the Group of Isometries on a Locally Compact Metric Space. Journal of Lie theory, Tome 13 (2003) no. 1, pp. 7-12. http://geodesic.mathdoc.fr/item/JLT_2003_13_1_JLT_2003_13_1_a1/