The documentation only mentions nested types, but it\'s not clear if they can be used as namespaces. I haven\'t found any explicit mentioning of namespaces.
Swift uses modules much like in python (see here and here) and as @Kevin Sylvestre suggested you can also use the nested types as namespaces.
And to extend the answer from @Daniel A. White, in WWDC they were talking about the modules in swift.
Also here is explained:
Inferred types make code cleaner and less prone to mistakes, while modules eliminate headers and provide namespaces.