Mathematics
Topological Spaces and Continuous Functions
Quick fact
The definition of a topological space was first formalized by Felix Hausdorff in 1914, but the concept of open sets was already implicit in the work of Henri Poincaré and Georg Cantor, and it took decades for the field to mature into an abstract discipline.
Why this is interesting
You've seen how to describe when a function is continuous on the real line. But what if you want to talk about continuity on a sphere, a donut, or a space with no notion of distance at all?