Some more:

4) Every nation has some defined set of borders. (The Yemen-Saudi Arabia border was only recently agreed, and was previously left deliberately ambiguous.)

5) Countries do not overlap. (Counterexample: France and Spain agree they both own Pheasant Island in the Pyrenees. The administration cycles every six months.)

6) Borders are at fixed coordinates. (Except for some borders defined by a river, which change when the river shifts its course. Some subnational borders are certainly like this.)

7) A nation's borders can be drawn with a single stroke of the pen. (Counterexample: South Africa takes two, one for the outside and one for its enclave Lesotho.)