: Generalizing the idea of distance to "open sets," allowing for the study of properties preserved under stretching or bending.
: Seeing how a professional mathematician structures a proof for a theorem—such as the Bolzano-Weierstrass property—is educational in itself. Introduction To Topology Mendelson Solutions
: In Mendelson's world, 90% of a proof is usually just applying the definition correctly. If you're stuck, re-read the definition of "Homeomorphism" or "Closure". : Generalizing the idea of distance to "open