One can even define topologies on graphs! Some interesting (semi-related) stuff! Please add Turning the sphere inside out: http://video.google.com/videoplay?docid=-6626464599825291409 The Topological Zoo http://www.geom.uiuc.edu/zoo/ Thomae's and Dirichlet functions discussed in week 5. And, we're not quite there yet, but very interesting nevertheless: the topologist's sine curve . Hitler Learns Topology Video: http://www.youtube.com/watch?v=SyD4p8_y8Kw