for X being non empty TopSpace
for f1 being Function of X,R^1 st f1 is continuous & ( for q being Point of X ex r being Real st
( f1 . q = r & r >= 0 ) ) holds
ex g being Function of X,R^1 st
( ( for p being Point of X
for r1 being Real st f1 . p = r1 holds
g . p = sqrt r1 ) & g is continuous )