Connected components of definable groups, and o-minimality II
نویسندگان
چکیده
In this sequel to [3] we try to give a comprehensive account of the “connected components” G00 and G000 as well as the various quotients G/G00, G/G000, G00/G000, for G a group definable in a (saturated) ominimal expansion of a real closed field. Key themes are the structure of G00/G000 and the problem of “exactness” of the G 7→ G00 functor. We prove that the examples produced in [3] are typical, and that for any G, G00/G000 is naturally the quotient of a connected compact commutative Lie group by a dense finitely generated subgroup (where we allow the trivial Lie group).
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ورودعنوان ژورنال:
- Ann. Pure Appl. Logic
دوره 166 شماره
صفحات -
تاریخ انتشار 2015