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I am an undergraduate math major with a focus in pure math. I have taken one semester of real analysis but we only briefly mentioned topology. I am wondering do I need to take topology and a second semester of real analysis(or is one semester good enough) in order to prepare for graduate school? Another route is to take complex analysis in place of topology. Thanks for help

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marked as duplicate by Zev Chonoles, Thomas Andrews, Ian Coley, vonbrand, M Turgeon Feb 11 at 1:35

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If you want to study pure maths you HAVE TO know general topology. I may say that every field of modern maths uses topology results.

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Topology is a pretty basic thing, every mathematician should know it, but it would be not too late to take it in the graduate school. This is how i had it myself. –  Alexey Feb 10 at 22:29
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@Emin Would studying from schaums topology be sufficient? –  d32 Feb 10 at 22:29
    
@ Alexey what math courses had you taken before your topology course in grad school? –  d32 Feb 10 at 22:31
    
Yes. Shaum's book is a good one for learning main things in general topology. –  Emin Feb 10 at 22:31
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@d32 i do not remember having taken more than one semester of real analysis, but i am not sure. In any case, i think it should be completely up to you to decide what to take, and even in the graduate school you will normally have choices. I think any recommendation should be based not on the course subject, but on who teaches it and on what you are currently interested in. –  Alexey Feb 10 at 22:50

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