Topology Exercises Books
Solution 1:
Fundamentals of General Topology: Problems and Exercises, Arkhangel'skii A., Ponomarev V.
Elementary topology, problem textbook, Viro O., Ivanov O., Netsvetaev N., Kharlamov V.
The topology problem solver, The Staff of REA
Solution 2:
This one is very nice:
Counterexamples in Topology, by Steen & Seebach.
Solution 3:
Another interesting one which illustrates lots of problems is:
Schaums Outline of General Topology by S. Lipschutz