Topology exercises
Solution 1:
Elementary Topology Problem Textbook O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov, is available freely online at
- http://www.pdmi.ras.ru/~olegviro/topoman/eng-book-nopfs.pdf
This book is published by AMS and that comes with solutions.
Solution 2:
"Fundamentals of General Topology: Problems and Exercises" by A. V. Arkhangel'skii; V.I. Ponomarev is a fun book, though it might be hard to find and the level might be higher than you'd like.
Solution 3:
I'd recommend "Elementary Topology Problem Textbook" by Viro, Ivanov, Netsvetaev, Kharlamov.