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    $\begingroup$ I am with you there Deane. $\endgroup$ Commented Mar 23, 2010 at 23:17
  • $\begingroup$ Charlie, I voted for your answer, too! $\endgroup$ Commented Mar 23, 2010 at 23:19
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    $\begingroup$ If this was really the rule, I never would have learned any analysis at all. In the context of analysis there were simply too many details floating around for me to see what was relevant and what wasn't. It made next to no sense to me until I learned a bit of topology, which set aside the parts that don't matter and let me focus on what was actually relevant. At that point I was able to go back and learn the analytic concepts quite easily, but without the chance to study general topology I don't think I could have. $\endgroup$ Commented Feb 5, 2014 at 20:10
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    $\begingroup$ It's very hard to appreciate compactness as a concept in its own right in a context where it just means "closed and bounded." $\endgroup$ Commented Feb 5, 2014 at 20:11