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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 ^_^

G. Chiusole
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HallaSurvivor
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    As for reasons, topological groups and topological rings are different topics, similar to how groups and rings are different topics. Although you do some elementary textbooks that cover both groups and rings, the topological versions of those two topics are more advanced, which makes it less likely to find one book covering them both. – Lee Mosher Mar 06 '20 at 20:42

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