  Three philosophical principles are often quoted in connection with Leibniz:
"objects sharing the same properties are the same object", "everything can
possibly exist, unless it yields contradiction", "the ideal elements correctly
determine the real things". Here we give a precise formulation of these
principles within the framework of the Topological Extensions of [8],
structures that generalize at once compactifications, completions, and
nonstandard extensions. In this topological context, the above Leibniz's
principles appear as a property of separation, a property of compactness, and a
property of analyticity, respectively. Abiding by this interpretation, we
obtain the somehow surprising conclusion that these Leibnz's principles can be
fulfilled in pairs, but not all three together.
