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A friend of mine, who likes math and knows I do too, told me he thinks topology is really cool. So, I was wondering if someone could suggest to me some good introductory topology books. Thanks in advance!

Danny
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You can suggest; Topology Without Tears

by

Sidney A. Morris; http://www.topologywithouttears.net/

user159888
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"Topology" by Munkres is a standard topology textbook which will give you the basics of the core parts of topology. Though I find the exercises in the book to be insufficient, I personally find "Foundations of Topology" to be a good supplement as well chapter 2 in "Principles of Mathematical Analysis" by Rudin for practice problems.