let X be non empty TopSpace; :: thesis: for A being Subset of X
for X0 being non empty SubSpace of X st the carrier of X0 misses A holds
(modid X,A) | X0 is continuous Function of X0,(X modified_with_respect_to A)
let A be Subset of X; :: thesis: for X0 being non empty SubSpace of X st the carrier of X0 misses A holds
(modid X,A) | X0 is continuous Function of X0,(X modified_with_respect_to A)
let X0 be non empty SubSpace of X; :: thesis: ( the carrier of X0 misses A implies (modid X,A) | X0 is continuous Function of X0,(X modified_with_respect_to A) )
assume the carrier of X0 misses A ; :: thesis: (modid X,A) | X0 is continuous Function of X0,(X modified_with_respect_to A)
then for x0 being Point of X0 holds (modid X,A) | X0 is_continuous_at x0 by Th109;
hence (modid X,A) | X0 is continuous Function of X0,(X modified_with_respect_to A) by Th49; :: thesis: verum