Joe N says: >If you want to combine two open intervals into a line segment, you need to add a single point (drop of glue). If one end already has that drop, you are good to go.
Actually, I think we can improve on this a bit. Rather than thinking of "glue", think of open ends and closed ends line segments as being like plugs: closed (male) to open (female). To plug them together you need to mate male to female or vice versa. And for these purposes a single point will also act like a two-sided male plug adapter.