A simple ohmmeter can made of Wheatstone's bridge with a variable resistance. An unknown resistance should be put into one of the shoulders of the bridge:
One can use a galvanometer to see whether the circuit is balanced or not. Changing the variable resistance it is possible to get zero current in the galvanometer. As soon as the current is 0, one can use an equation
to find the unknown resistance.
To figure out whether the terminals are opened, calculate the circuit for :
In the case the circuit is balanced, that current is 0, and it has any other value if the terminals are closed but the circuit is unbalanced.