I am a university graduate with a B.S. in mathematics who has been developing software for the past 8 years. I recently discussed a mutual interest in topology with a friend who is just about to complete his degree. Due to time constraints both of us missed our chance to take a topology course during our undergraduate studies, so we have decided to make an independent study of the subject once he finishes school, and are looking for a book to guide us.
Ideally I am looking for a book that...
- is suitable for our math background
- is well laid out and not too difficult to follow (i.e. is suited to self study)
- does not assume prior knowledge
- is thorough enough to enable future study of topics within the field
- contains plenty of exercises
- isn't sparse on diagrams where they are appropriate
- doesn't waste much time on overly-specific material (I'm the type that likes to prove things about the determinant, not calculate thousands of them)