Which would fit this description and with answers?
I found the one in the Schaum Outline series (by Lipshutz) very easy to learn from.
i learned more than enough general topology for a lifetime, from the book entitled general topology by kelley. after a short while it became clear that "real" topology is algebraic or differentiable topology.
if you like old books, the one called set theory by hausdorff is wonderful.
oh you said with answers. unfortunately good books do not have answers. Indeed the ability to enjoy questions without answers is pretty much the mark of someone with the potential to do research.
There is a book called REA's Problem Solvers, and there is a topology book with hundreds of solutions to Topology problems. However the material is quite weak outside of the problems. I would recommend Topology by Munkres to get the "lecture" part. I know this is used as a graduate level textbook, but it doesn't really require a "deep" math background.
try "counterexamples in topology", a book full of interesting strange examples with short proofs. actually i liked "counterexamples in analysis" better, especially as a college freshman, and many of those are also somewhat topological.
I learned the basics from Mendelson's "Introduction to Topology, Second Edition." It's published by Dover for less then $15, even.
for me topology only got started being interesting when i figured out how to prove that a continuous function from the unit disc to the plane which equals the identity on the unit circle, must map something to 0.
i.e. try and prove the fundamental theorem of algebra by topology.
Crossley's "Essential Topology" in the Springer Undergraduate Math Series. Answers to selected exercises are included - as is the norm for SUMS books.
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