Modern treatment of Topology that focuses on intuition and is full of explanations and visual insights.

Question

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.

Answer 1

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.