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I'm interested in a modern treatment of Topology (point-set, and general topology at the undergraduate level) that focuses on intuition and is full of explanations and visual insights. This will be meant as a first exposure to topology.

There's the classic topology by Munkres, but I find it a bit unintuitive sometimes, so I'm looking for an alternative.

I'm looking for a book that has the same style as Needham's Visual Complex Analysis.

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    $\begingroup$ What kind of topology? Point set topology? Algebraic topology? What level? A first exposure to topology, or something else? Personally I love Thurston's "Three dimensional geometry and topology" for its intuitive explanations and insights, but it is quite dense for a first exposure to topology. $\endgroup$ – Steven Gubkin Jan 2 '15 at 19:42
  • $\begingroup$ @StevenGubkin point set topology (intro to advanced lvl) + general topo (intro and for undergrad) i said that in my question $\endgroup$ – user153330 Mar 14 '15 at 15:06
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    $\begingroup$ In fact, it appears that you edited that information into your question back in response to my comment back in January. Originally it was absent. $\endgroup$ – Steven Gubkin Mar 14 '15 at 16:28
  • $\begingroup$ @StevenGubkin okay sorry for that $\endgroup$ – user153330 Mar 15 '15 at 15:53
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You could start with Flegg's From Geometry to Topology. It may not be extremely modern, but it is well-illustrated and prepares the ground for general topology.

Another possibility is Richeson's Euler's Gem, which is indeed a gem of a book and gently leads into topology by way of Euler's polyhedral formula.

A modern follow-up would be Introduction to Topology: Pure and Applied by Adams and Franzosa. It's full of illustrations and applications, and can certainly be used as a first exposure to point-set topology.

Then, if you wish, you can whet your appetite for more advanced topics with Ghrist's Elementary Applied Topology. Plenty of illustrations again.

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  • $\begingroup$ Can you specify for me a specific order in which to read these books? Can I just read them while taking notes from Munkres? $\endgroup$ – user153330 Jan 2 '15 at 19:54
  • $\begingroup$ @user153330: Flegg is a short book that you can read before starting Munkres or Adams & Franzosa (or an equivalent book). In fact, it's designed that way. Richeson can be read at any stage in a relaxed way. Adams & Franzosa overlaps Munkres in much of the material and can be read concurrently, complementing the latter with its applied sections. Ghrist is perhaps best read when you have some general topology under your belt and are getting ready to delve into more advanced topics and applications. Much of the actual delving will require consulting other books. $\endgroup$ – J W Jan 2 '15 at 21:33

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