Groups definable in linear o-minimal structures: the non-compact case. (English) Zbl 1184.03034

Summary: Let \(\mathcal M=\langle M, +, <, 0, S\rangle \) be a linear o-minimal expansion of an ordered group, and \(G=\langle G, \oplus , e_{G}\rangle \) an \(n\)-dimensional group definable in \(\mathcal M\). 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 \(\vee \)-definable subgroup \(U\) of \(\langle M^{n}, +\rangle \) and a lattice \(L\) of rank equal to the dimension of the ‘compact part’ of \(G\).


03C64 Model theory of ordered structures; o-minimality
46A40 Ordered topological linear spaces, vector lattices
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