theorem Th57: :: JORDAN2C:73

for n being Nat
for r being Real
for p, p1, p2 being Point of (TOP-REAL n)
for u being Point of (Euclid n)
for f being Function of I[01],(TOP-REAL n) st f is continuous & f . 0 = p1 & f . 1 = p2 & p in Ball (u,r) & p2 in Ball (u,r) holds
ex h being Function of I[01],(TOP-REAL n) st
( h is continuous & h . 0 = p1 & h . 1 = p & rng h c= (rng f) \/ (Ball (u,r)) )