Completeness of locally \(k_{\omega}\)-groups and related infinite-dimensional Lie groups (Q2401566)

The main result of this paper asserts that a topological group is complete whenever the underlying topological space is locally \(k_{\omega}\). The latter means that each point of the space has an open neighbourhood which is the direct limit of an ascending sequence of compact Hausdorff topological spaces. As a consequence of this result, it is shown that every infinite-dimensional Lie group modelled on a Silva space is complete.