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I am looking for a short topology document,which is roughly 60-80 pages long and touches on metric spaces,open and closed sets,perfect,bounded sets,limit points,compact,perfect and connected sets.

Can anyone please point me to such a resource?I intend to use it primarily as preparation for study of real analysis. Figures and illustrations with proper proofs will be perfect.

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4 Answers

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I like Marsden's "Elementary classical analysis". The first 80 or so pages cover much of what you mentioned. Lots of exercises, focus on understanding.

I like the metric spaces section in Kolmogorov & Fomin's "Introductory Real Analysis".

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Marsden's text seems fine.Thanks. –  Richard Nash Dec 10 '12 at 20:10
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Mendelson's Introduction to Topology is concise and serves well as preparation for a Real Analysis course. It's also very cheap. I highly recommend it.

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Topology, by Munkres. Just read the relevant sections.

One of the most well-written math books IMO.

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My first introduction to topology came through Willard's General Topology. It's a little more in depth than what you've asked for, but you can always just skim the relevant sections. It's a fantastic, highly readable account. In addition, Rudin's PoMA section on topology covers the bare essentials of what you're looking for in the context of real analysis.

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Rudin seems to make few concessions when it comes to infusing some intuition.I really want to avoid that book as my first introduction to topology. –  Richard Nash Dec 10 '12 at 19:52
    
I would violently agree with this. –  copper.hat Dec 10 '12 at 20:07
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