for X being non empty TopSpace
for X1, X2 being non empty SubSpace of X holds
( X1,X2 are_separated iff ( X1 misses X2 & ( for Y being non empty TopSpace
for f1 being continuous Function of X1,Y
for f2 being continuous Function of X2,Y holds f1 union f2 is continuous Function of (X1 union X2),Y ) ) )