for n, m being Nat
for T1, T2 being non empty TopSpace
for A being convex non boundary compact Subset of (TOP-REAL n)
for B being convex non boundary compact Subset of (TOP-REAL m)
for C being convex non boundary compact Subset of (TOP-REAL (n + m))
for f being Function of T1,((TOP-REAL n) | A)
for g being Function of T2,((TOP-REAL m) | B) st f is being_homeomorphism & g is being_homeomorphism holds
ex h being Function of [:T1,T2:],((TOP-REAL (n + m)) | C) st
( h is being_homeomorphism & ( for t1 being Point of T1
for t2 being Point of T2 holds
( ( f . t1 in Int A & g . t2 in Int B ) iff h . (t1,t2) in Int C ) ) )