Lie Theory and the Structure of pro-Lie groups and pro-Lie algebras

This text presents basic results from a projected monograph on "Lie Theory and the Structure of Pro-Lie groups and Locally Compact Groups" which may be considered a sequel to our book "The Structure of Compact Groups" [De Gruyter, Berlin, 1998]. In focus are the categories of projective limits of finite dimensional Lie groups and of projective limits of finite dimensional Lie algebras, their functorial relationship, and their intrinsic Lie theory. Explicit information on pro-Lie algebras, simply connected pro-Lie groups and abelian pro-Lie groups is given.