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 holds
ex E being non empty Subset of I[01] ex f being Function of (I[01] | E),((TOP-REAL n) | A) st
( E = [.a,b.] & f is being_homeomorphism & f . a = p & f . b = q )