theorem Th24: :: JORDAN2C:37

for n being Nat
for w1, w2, w3 being Point of (TOP-REAL n)
for P being non empty Subset of (TOP-REAL n)
for h1, h2 being Function of I[01],((TOP-REAL n) | P) st h1 is continuous & w1 = h1 . 0 & w2 = h1 . 1 & h2 is continuous & w2 = h2 . 0 & w3 = h2 . 1 holds
ex h3 being Function of I[01],((TOP-REAL n) | P) st
( h3 is continuous & w1 = h3 . 0 & w3 = h3 . 1 )