theorem Th46: :: BORSUK_4:49

for n being Element of NAT
for A being Subset of (TOP-REAL n)
for p, q being Point of (TOP-REAL n)
for a, b being Point of I[01] st A is_an_arc_of p,q & a < b & b <> 1 holds
ex E being non empty Subset of I(01) ex f being Function of (I(01) | E),((TOP-REAL n) | (A \ {p})) st
( E = ].a,b.] & f is being_homeomorphism & f . b = q )