What is Topology?

An entry-level primer on "rubber-sheet geometry"

When I studied topology as an undergraduate, I always found it difficult to answer the inevitable question from family and friends:

“What on Earth is topology?”

Every time, I would give them a slightly different answer, but I was never really satisfied with any of explanations. If you’ve ever googled topology, you will have no doubt encountered the animation of a doughnut morphing into a coffee mug. Most explanations I gave involved something related to this animation; how in topology a doughnut and a coffee mug are the same or how a sphere and a cube are the same. But an answer like this doesn’t really tell anyone what topology is really about, what is involved in actually working with topology nor explain why it’s even a worthwhile pursuit. Continue reading


Read the full essay in Cantor’s Paradise on Medium