Reference for general-topology

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.

Stephen Willard, General Topology

This book is less complete than Engelking, but still contains enough material to make a good reference book. It is also quite cheap, as a Dover book.

The following 3 volume set (translated from Russian, edited by A. V. Arhangelskii) deserves to be mentioned among references for general topology, too. It is part of Encyclopaedia of Mathematical Sciences series.

• General topology. I. Basic concepts and constructions. Dimension theory. Encyclopaedia of Mathematical Sciences, 17. Springer-Verlag, Berlin, 1990. ISBN 3-540-18178-4 Google Books link, DOI:10.1007/978-3-642-61265-7_1, MR1077251

• General topology. II. Compactness, homologies of general spaces. Encyclopaedia of Mathematical Sciences, 50. Springer-Verlag, Berlin, 1996. ISBN 3-540-54695-2 Google Books link, DOI:10.1007/978-3-642-77030-2, MR1392480

• General topology. III. Paracompactness. Function spaces. Descriptive theory. Encyclopaedia of Mathematical Sciences, 51. Springer-Verlag, Berlin, 1995. ISBN 3-540-54698-7 Google Books link, DOI:10.1007/978-3-662-07413-8, MR1416131.