This is not a question regarding a specific mathematics problem, rather I am looking for some good texts that go into detail on the weak topology. My exposure to weak topologies is via Banach spaces but I would like to find a textbook that deals with weak topologies for general topological spaces as well as Banach spaces. Does anyone know of such textbooks? I already have a copy of Brezis as well as Rudin's functional analysis.
2026-03-26 01:07:35.1774487255
Textbook recommendations for weak topology
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Books on linear topological spaces are probably what you're looking for. In a sense, a LTS (or a TVS, topological vector space) is what underlies a Banach space as that requires completeness which is not always available.
Two I can definitely recommend are:
Linear Topological Spaces by Kelley and Namioka (et al) -- it's a SpringerVerlag book and the link is to the Springer website; you may find copies in a library, or cheaper elsewhere.
Topological Vector spaces and their applications by Bogachev and Smolyanov -- also SpringerVerlag and that link includes a free preview of the book.
Of the two, I prefer Bogachev which has a very clean, analytical style and is more recently written. Both books are comprehensive, and both cover substantially more than just the weak topology.