for n being Nat
for X being non empty SubSpace of TOP-REAL n
for f being Function of X,R^1 st f is continuous holds
ex g being Function of X,(TOP-REAL n) st
( ( for a being Point of X
for b being Point of (TOP-REAL n)
for r being Real st a = b & f . a = r holds
g . b = r * b ) & g is continuous )