for T being T_2 TopSpace
for P, Q being Subset of T
for p being Point of T
for f being Function of I[01],(T | P)
for g being Function of I[01],(T | Q) st P /\ Q = {p} & f is being_homeomorphism & f . 1 = p & g is being_homeomorphism & g . 0 = p holds
ex h being Function of I[01],(T | (P \/ Q)) st
( h is being_homeomorphism & h . 0 = f . 0 & h . 1 = g . 1 )