Alan Winfield

What sets a subway map apart from other kinds of maps? Why does a knot get tangled up? Why is the Möbius strip skewed in one direction? These topological investigations involve the mathematical analysis of the properties that persist when objects are bent or stretched. In the 20th century, topology developed and became as fundamental as algebra and geometry, with important implications for science, notably physics.

Richard Earl explores the formal concept of continuity and some of the more aesthetically pleasing topology features in this Very Short Introduction (looking at surfaces). By considering some of the eye-opening situations that helped mathematicians realize a need for studying topology, he pays homage to the historical individuals, problems, and surprises that have spurred the development of this discipline.