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I took 2 semester course on point set topology, also studied it on my own and learned some basic algebraic topology from Hatcher's book. It has been a while since my last topology study. Now, I want to study some further topics in topology. I can still prove some basic theorems like "compactness is preserved under continuous functions". However, I do not remember how to approach more complicated theorems so I need a quick recap. I do not want to dive into a book-since I am not starting it from "0"- therefore I am looking for some lecture notes that can help me to see what is going on and gain some speed while doing proofs. Thank you.

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  • $\begingroup$ Bredon's (topology and geometry) first chapter is an excellent recap and reference for the basics of topology. $\endgroup$ – Aloizio Macedo Mar 26 '17 at 21:54
  • $\begingroup$ @AloizioMacedo, Thank you, I am checking it now. $\endgroup$ – Ninja Mar 26 '17 at 22:02
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    $\begingroup$ why not recap the points you aren't comfortable with as they come up in your further study? $\endgroup$ – Teman Mar 27 '17 at 16:16
  • $\begingroup$ @mt3, the lecture notes looks more "smooth" to me, on the other hand in a reference book there are bunch of theorems, examples written in a small font that looks -in my conditions- unnecessarily complicated to me. $\endgroup$ – Ninja Mar 27 '17 at 19:09

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