I am interested in using the history of point set topology to inform the way we teach topology. Topology often feels far removed from other areas of math, and it is simply a hard area of math to motivate. I remember that when my undergraduate topology professor first introduced us to compactness, he said "Here is a definition that no one in their right mind would ever write down!" Part of my goal in working on primary source projects in topology is to avoid giving students definitions that "no one in their right mind would write down." Rather, when it is time to write down the definitions, I want what we write down to be natural and well-motivated. Focusing on how certain topics developed historically can be a way to achieve this goal.
Much of my interest has been on the historical development of point-set topology proper; that is, concepts like connectedness, the derived set, nowhere dense sets, limit points, etc. from 1872-1920s. This development is embodied in the works of authors such as Cantor, Frechet, Kuratowski, R.L. Moore, Jordan, Riesz, and many others. For TRIUMPHS grant, I plan to write 6 mini projects and 2 full length projects. I will be using the original writings of many of the authors listed above.