I know that there is a large body of knowledge regarding groups/rings/modules/fields/etc. endowed with topologies, but I'm struggling to find references for them.
I have heard of a few books, which are mostly restricted to one of the above structures, for instance:
- Husain's "Introduction to Topological Groups"
- Pontryagin's "Topological Groups"
- Warner's "Topological Rings"
- Arnautov, Glavatsky, and Mikhalev's "Introduction to the Theory of Topological Rings and Modules"
But I am not sure if there is a book that covers the basics of topological algebra in the same way that, for instance, Dummit and Foote covers non-topological algebra.
Is there a good book which covers the basics of topological algebraic structures broadly? If not, is there a reason such a reference doesn't exist? Also if not, what books would you recommend for topological groups/actions and rings/modules?
Thanks in advance ^_^