Journal of Symbolic Logic 75 (1):208-220 (2010)

Abstract
Let $\scr{M}=\langle M,+,<,0,S\rangle $ be a linear o-minimal expansion of an ordered group, and $G=\langle G,\oplus ,e_{G}\rangle $ an n-dimensional group definable in $\scr{M}$ . We show that if G is definably connected with respect to the t-topology, then it is definably isomorphic to a definable quotient group U/L, for some convex ${\ssf V}\text{-definable}$ subgroup U of $\langle M^{n},+\rangle $ and a lattice L of rank equal to the dimension of the 'compact part' of G
Keywords O-minimal structures   Quotient by lattice
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DOI 10.2178/jsl/1264433916
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Type-Definability, Compact Lie Groups, and o-Minimality.Anand Pillay - 2004 - Journal of Mathematical Logic 4 (02):147-162.

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Non-Standard Lattices and o-Minimal Groups.Pantelis E. Eleftheriou - 2013 - Bulletin of Symbolic Logic 19 (1):56-76.

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