theorem Th47: :: JORDAN6:47

for P being Subset of (TOP-REAL 2)
for Q being Subset of ((TOP-REAL 2) | P)
for p1, p2 being Point of (TOP-REAL 2) st P is being_simple_closed_curve & p1 in P & p2 in P & p1 <> p2 & Q = P \ {p1,p2} holds
not Q is connected