theorem Th29: :: JORDAN2C:42

for n being Nat
for a being Real
for Q being Subset of (TOP-REAL n)
for w1, w4 being Point of (TOP-REAL n) st Q = { q where q is Point of (TOP-REAL n) : |.q.| > a } & w1 in Q & w4 in Q & ( for r being Real holds
( not w1 = r * w4 & not w4 = r * w1 ) ) holds
ex w2, w3 being Point of (TOP-REAL n) st
( w2 in Q & w3 in Q & LSeg (w1,w2) c= Q & LSeg (w2,w3) c= Q & LSeg (w3,w4) c= Q )