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.
Cheers.
———————update———————–
Thanks for all the delightful replies.
I will try to quickly check the books mentioned beneath.
And I may accept the answer which is most closed to my personal flavor.
Sorry for others.
It's a pity no multiple acceptance can be made for such a ref-request question.
Greetings.
Best Answer
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.