let X be non empty TopSpace; :: thesis: for X0, X1 being non empty SubSpace of X st X0 misses X1 holds
(modid X,X0) | X1 is continuous Function of X1,(X modified_with_respect_to X0)
let X0, X1 be non empty SubSpace of X; :: thesis: ( X0 misses X1 implies (modid X,X0) | X1 is continuous Function of X1,(X modified_with_respect_to X0) )
assume X0 misses X1 ; :: thesis: (modid X,X0) | X1 is continuous Function of X1,(X modified_with_respect_to X0)
then for x1 being Point of X1 holds (modid X,X0) | X1 is_continuous_at x1 by Th118;
hence (modid X,X0) | X1 is continuous Function of X1,(X modified_with_respect_to X0) by Th49; :: thesis: verum