"Though there are several posts discussing the reference books for topology, for example best book for topology. But as far as I looked up to, all of them are for the purpose of learning topology or rather on introductory level. I am wondering if there is a book or a set of books on topology like Rudin's analysis books, S.Lang's algebra, Halmos' measure (or to be more updated, Bogachev's measure theory), etc, serving as standard references.

Jocelyn Bernard 2022-09-06 Answered
Though there are several posts discussing the reference books for topology, for example best book for topology. But as far as I looked up to, all of them are for the purpose of learning topology or rather on introductory level.
I am wondering if there is a book or a set of books on topology like Rudin's analysis books, S.Lang's algebra, Halmos' measure (or to be more updated, Bogachev's measure theory), etc, serving as standard references.
Probably, such a book should hold characteristics such as being self-contained, covering the most of classical results, and other good properties you can name.
In the end, I only have the interest on general-topology (topological space, metrization, compactification...), and optionally differential topology (manifolds). So please don't divert into algebraic context.
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Answers (2)

Nolan Tyler
Answered 2022-09-07 Author has 9 answers
For general topology, it is hard to beat Ryszard Engelking's "General Topology". It starts at the very basics, but goes through quite advanced topics. It may be perhaps a bit dated, but it is still the standard reference in general topology.
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pokvarilaap
Answered 2022-09-08 Author has 3 answers
The Handbook of Set-Theoretic Topology is a great reference on many advanced areas of general topology.
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