:: deftheorem Def10 defines modified_with_respect_to TMAP_1:def 10 :
for X being non empty TopSpace
for X0 being SubSpace of X
for b₃ being strict TopSpace holds
( b₃ = X modified_with_respect_to X0 iff for A being Subset of X st A = the carrier of X0 holds
b₃ = X modified_with_respect_to A );