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- Thread starter huyichen
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- #2

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For the most part, books like that one will take the same darned examples and use them over and over again. There are more exotic spaces with less intuitive properties (such as L^infinity), but even those examples tend to get reused in the book.

- #3

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- #4

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and of course,

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As far as textbooks, my favorite is the trilogy by John M Lee starting with:

and there are many Dover entries. For example:

is very approachable (more so than Willard).

Finally the two MIT classics are the undergrad texts by Munkres and Singer & Thorpe.

All of the above assumes a background in real analysis "There's a delta for every epsilon" right? If that's new to you, Real Analysis by Frank Morgan is a great introduction. Don't try to push brute force through point set topology without knowledge of real analysis.

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I like *Topology* by Janich. It gets the intuition across, but it doesn't have any exercises.

- #7

vici10

http://books.google.ca/books?id=AVV...resnum=3&ved=0CA4Q6AEwAg#v=onepage&q=&f=false

The problems are ranged from simple to very complex, some are still open. The solutions to the problems at the back of the book.

- #8

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why do you want to study topology? I think the general conceptions is useless in physics.if you don't use it ,you can't master it.it is just waste of time for physicists to study it. you 'd better abandon it.

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- #9

George Jones

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why do you want to study topology? I think the general conceptions is useless in physics.if you don't use it ,you can't master it.it is just waste of time for physicists to study it. you 'd better abandon it.

'

Are you serious?

Firstly, this a topology forum.

Secondly, huyichen, the original poster in this thread has not mentioned physics, and might have no interest in physics. For example, for all we know, huyichen could be a pure mathematician or a student of pure mathematics who has no interest in physics.

Thirdly, topology is used in various areas of mathematical physics, e.g. the global methods used in general relativity. I think it would be difficult to read the proofs in Hawking and Ellis with understanding without some knowledge of topology.

For example, it's easy to show using a topological argument,

https://www.physicsforums.com/showthread.php?p=1254758#post1254758,

that any compact spacetime must have closed timelike curves (time travel).

- #10

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personally I advise you to learn general topology as you need it in other areas of mathematics. usually a first course in complex analysis will give you a strong start.

- #11

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Are you serious?

Firstly, this a topology forum.

Secondly, huyichen, the original poster in this thread has not mentioned physics, and might have no interest in physics. For example, for all we know, huyichen could be a pure mathematician or a student of pure mathematics who has no interest in physics.

Thirdly, topology is used in various areas of mathematical physics, e.g. the global methods used in general relativity. I think it would be difficult to read the proofs in Hawking and Ellis with understanding without some knowledge of topology.

For example, it's easy to show using a topological argument,

https://www.physicsforums.com/showthread.php?p=1254758#post1254758,

that any compact spacetime must have closed timelike curves (time travel).

Thanks a lot!your criticism opened my vision. Now I just read books about differential geometry in physics.I am just a student.

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