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May 16th, 2013, 01:43 PM   #1
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Where to start with topology?

Hello everybody,

recently i have become interested in topology, and only lately I got the time to look into the subject. I'm heading for my first year of university in september in mathematics.

I'm finishining the IB Mathematics HL now, and so i thought i could continue on to something new already .

and so here comes my question;

does anyone know any resources where i could start learning the topic?

Preferably any books, that would explain the introductory concepts (best if available online! free or not, both fine )
with some problems to maybe actually test my understanding, or maybe video resources?

to start with i have some knowledge of calculus, basics of group theory.

If i need some preliminary topics before going to topology, it would be great if you could suggest resources on those too

I am aware that my level of math might not be highest, as I am not even a uni student yet, however I am willing to learn and would really appreciate your help in giving any directions. The internet is overloaded with information and because o this i can't really even see where to start with this subject!

Thanks for any help in advance
casualic is offline  
 
May 16th, 2013, 03:05 PM   #2
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Re: Where to start with topology?

It's helpful that you know some group theory.

At the elementary level there are essentially two aspects of topology: general topology, where you study the spaces you get when you abstract the notion of an open set; and algebraic topology, where you apply abstract algebra to the study of various types of spaces.

Most people start with general topology. But if you just want to get going and don't mind jumping in a little over your head, you might look at algebraic topology. Perhaps look at some Wikipedia pages on the subject.

I think if you start here ...

http://en.wikipedia.org/wiki/Algebraic_topology

... and click on the linked articles, you'll get the flavor of the subject. Perhaps some of the references will be what you're looking for.
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May 25th, 2013, 05:19 PM   #3
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Re: Where to start with topology?

"Introduction to Topology" by Gameline and Greene should be a good start for you. Not only is meant to for beginners as obviously stated by the title, but also has entire solutions for each exercises at the end of sections, something of a rarity among math reference and textbooks.

If there's a downside, then it's that the book is relatively dry compared to the colorful math textbooks that you're probably used to from high school. Expect to draw graphics and examples by yourself. This is something to applies to almost every math reference you encounter beyond Calculus/Linear Algebra.
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June 18th, 2013, 09:49 PM   #4
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Re: Where to start with topology?

Where as I have checked out the reviews about the books about topology I would commander you Topology (2nd Edition) by James Munkres. It is actually an in depth coverage of both general topology and algebraic topology, includes example and figures.
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