Geodesic
Locally Precompact Groups: (Local) Realcompactness and Connectedness
Journal of Lie theory, Tome 20 (2010) no. 2, pp. 347-374.

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A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called "locally precompact. Within the class of locally precompact groups, the authors classify those groups with the following topological properties:
Classification : 22A05, 54H11, 22B05, 22C05
Mots-clés : Precompact group, precompactly generated group, locally precompact group, Weil completion, Dieudonn� complete group, locally Dieudonn� complete group, realcompact group, locally realcompact group, connected group, locally connected group, omega-balanced g 
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     author = {W. W. Comfort and G. Luk�cs },
     title = {Locally {Precompact} {Groups:} {(Local)} {Realcompactness} and {Connectedness}},
     journal = {Journal of Lie theory},
     pages = {347--374},
     publisher = {mathdoc},
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     number = {2},
     year = {2010},
     url = {http://geodesic.mathdoc.fr/item/JLT_2010_20_2_JLT_2010_20_2_a6/}
}
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W. W. Comfort; G. Luk�cs . Locally Precompact Groups: (Local) Realcompactness and Connectedness. Journal of Lie theory, Tome 20 (2010) no. 2, pp. 347-374. http://geodesic.mathdoc.fr/item/JLT_2010_20_2_JLT_2010_20_2_a6/