I like when mathematicians do names right
the concept of a connected set is exactly what you think of when you see the words connected set
then you go and add "doubly connected set" and then the intuition all falls apart
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(it does still make sense if you see it like this though: in a simply connected set, any cut made between two points on the boundary results in an unconnected set. In a doubly connected set, though, there are cuts between boundary points that result in simply connected sets, meaning you can make two cuts before it becomes unconnected)
