The topic of topology is a bit difficult to explain, as I find it to be a bit abstract, but the Wikipedia article does a better job than I could. This is especially true since I am currently studying this and am not far enough along to have a good idea of what all the field encompasses. In a lot of ways it is a generalization of concepts in analysis, but I’m sure it is also much more than that.
The text I have chosen to use as an introduction to this topic is “Topology” by James Munkres, which is I understand is considered one of the best to use. This text assumes pretty much no knowledge of set theory and teaches what is needed in the first chapter. I have found that studying real analysis prior to this was very helpful in providing motivation for some of the material, though this would by no means be a necessity. As with most topics at the undergraduate level, having a solid understanding of logic and proofs is essential.
Resources
- Buy the text at Amazon (affiliate link)
- I am writing a solutions manual as I work through exercises. The source for this is available on GitHub. A PDF of the manual is built and published hourly as necessary, and can be downloaded here. Note that I am currently on a pure math hiatus so there will not be any updates to this for some time.
- Another excellent online solutions manual at dbFin
- Another solutions manual at GitHub