If there is no boundary to the surface of the earth as to be distinguished form the space that immediatley proceed it, then terms, ideas and concepts have on meaning at all.
The 2-D
surface of the Earth is unbounded. There is no outer-space on the surface to distinguish from. To even consider outer-space, you have to include an extra dimension i.e. "up" from the surface.
No boundary in the context of space could only mean limitless in any direction, correct?
If you're on the surface of the Earth and limited to 2-D (so you can only go north-south and east-west), how far do you have to go before you reach the limit of the surface?
There is no limit, you can just keep going around and around. It is unbounded.
Now, the 3-D universe could be unbounded in the same way, that no matter which way you go in 3 directions, you can just keep going around and around. But this doesn't mean that it is infinite just like the surface of the Earth is not infinite.