Topology, also known as rubber-sheet geometry, is actually a branch of mathematics that studies objects being distorted without being torn or cut.  We recently discovered Jill Britton’s web site, which is dedicated solely to math (and much of it to fun topology-related material).  Her R-U-B-B-E-R Geometry page is especially nice, providing many fascinating links to topology activities involving math, history, geography, science and art.