Recently started a topology course, I am struggling to visualise connected topological spaces in topology, I am understanding the definition when it comes to clopen subsets and disjointness, ie $[0,1) \cup (1,2]$ is disconnected.
Could someone give me a hand visualising this ( ie overlapping circles and how connectedness works in that sense) would it simply be two overlapping circles are connected if they intersect at some point?
The example I received was two overlapping circles completely shaded In apart from their intersection in the middle, $A$ and $B$ where connected but $A \cap B$ where not.
I would draw this if I knew how on here. Thanks