I'm going to take an introductory class on dynamical systems at the level of Guckenheimer & Holmes, or Arnold's ODEs book, but I don't have any topology background. I know analysis at the level of Stein's Fourier and Complex analysis, but have not had exposure to full-blown measure theory or manifolds. Is there a book that covers basic point-set topology in an accessible manner but perhaps without unneeded generality?
Thanks!