theorem Th39: :: JORDAN6:39

for n being Nat
for P, P1, P2 being Subset of (TOP-REAL n)
for Q being Subset of ((TOP-REAL n) | P)
for p1, p2 being Point of (TOP-REAL n) st P2 is_an_arc_of p1,p2 & P1 \/ P2 = P & P1 /\ P2 = {p1,p2} & Q = P1 \ {p1,p2} holds
Q is open