Get access

Groups, group actions and fields definable in first-order topological structures



Given a group (G, ·), GMm, definable in a first-order structure equation image equipped with a dimension function and a topology satisfying certain natural conditions, we find a large open definable subset VG and define a new topology τ on G with which (G, ·) becomes a topological group. Moreover, τ restricted to V coincides with the topology of V inherited from Mm. Likewise we topologize transitive group actions and fields definable in equation image. These results require a series of preparatory facts concerning dimension functions, some of which might be of independent interest.