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I want to know if anyone would recommend some website/book/source where I can begin learning about topology. Here is my situation:

Currently the highest level of math which I can take is a class on mathematical analysis/real analysis, which only briefly covers topology.

I want to know what sources I should use to introduce myself to topology and then go as far as I choose, and not be limited by material I have available.

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    $\begingroup$ Easy one: topology without tears; classic one: Munkre's Topology $\endgroup$ Commented Oct 1, 2018 at 20:19
  • $\begingroup$ Also Kosniowski: Introduction to algebraic topology is good for a first grasp of the basics of the subject, and then you can go on reading it and learning new staff. $\endgroup$ Commented Oct 1, 2018 at 20:39

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Take analysis to get a sense of limits and continuity. This will give intuition for topology which is a generalized notion of limits and continuity. Then study point set topology as suggested by GNU. Point set topology is about the texture of a space. Afterwards you could study algebraic topology which is about shape of flexible spaces such as does it have holes or knots. You will want a basic understanding of abstract algebra, at least groups, for algebraic topology.

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  • $\begingroup$ Although knowing analysis does help to learn topology, I don't think it's required beyond maybe the definition of continuity. Rudin basically has a chapter on topology earlier on, and that chapter is harder to read and leave more to the reader imo than anything in Munkres. Obviously analysis should be learned at some point anyway but I don't think it's a reason to put off topology if you are interested. $\endgroup$ Commented Oct 2, 2018 at 4:49
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Im my option the best way to start learning this subject would be "Point Set Topology" by B. Conway

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