The axiom of choice, Tychonoff's theorem, and the open mapping theorem [0, 1, 2]. Each one took me, in my view, much too long to grasp.

[0] https://en.wikipedia.org/wiki/Axiom_of_choice

[1] https://en.wikipedia.org/wiki/Tychonoff%27s_theorem

[2] https://en.wikipedia.org/wiki/Open_mapping_theorem_(function...