theorem Th22: :: TIETZE_2:22

for n being Nat
for T being TopSpace
for A being closed Subset of T st T is normal holds
for f being Function of (T | A),((TOP-REAL n) | (ClosedHypercube ((0. (TOP-REAL n)),(n |-> 1)))) st f is continuous holds
ex g being Function of T,((TOP-REAL n) | (ClosedHypercube ((0. (TOP-REAL n)),(n |-> 1)))) st
( g is continuous & g | A = f )