I'm having trouble understanding how deleting a point from R2 leaves it a connected space, while deleting a point from R doesn't do so.
Can someone help me with this?
Thanks,
MAX
This is one characterization of connect sets:
A set is connected if it is not the union of two non-empty separated sets.
Two sets are separated if neither contains a point or a limit point of the other.
Now , clearly the union of two separated sets.
Try that with . What two separated sets would be possible?