Continuity & Homeomorphisms – Lecture 15 (Topology)

From a purely topological standpoint, what does it intuitively mean for a function f : X → Y to be continuous?

1. A.It can be drawn without lifting your pencil from the paper
2. B.It preserves proximity: points close in X stay close in Y
3. C.It maps every open set to an open set in the codomain
4. D.It is differentiable at every point of its domain