Epilogue

Topology remains a large, active research area in mathematics. Unsurprisingly its character has changed over the last century—there is considerably less current interest in general topology, but whole new areas have emerged, such as topological data analysis to help analyze big data sets. The Epilogue concludes that the interfaces of topology with other areas have remained rich and numerous, and it can be hard telling where topology stops and geometry or algebra or analysis or physics begin. Often that richness comes from studying structures that have interconnected flavours of algebra, geometry, and topology, but sometimes a result, seemingly of an entirely algebraic nature say, can be proved by purely topological means.