1. What is topology?

Topology is now a major area of modern mathematics, but an appreciation of topology came late in the history of mathematics. The word topology—meaning ‘the study of place’—was not coined until 1836. ‘What is topology?’ aims to provide a sense of topology’s ideas and its technical vocabulary. It discusses the concepts of letters being topologically the same or homeomorphic and then moves on to Euler’s formula, which shows that there are only five Platonic solids: tetrahedron, cube, octahedron, dodecahedron, and icosahedron. Early problems in topology included defining what dimension means and point-set topology, which sought to address what it means to be a set or to be a space.