:: deftheorem Def10 defines u.s.c._decomposition BORSUK_1:def 10 :
for X being non empty TopSpace
for b₂ being non empty a_partition of the carrier of X holds
( b₂ is u.s.c._decomposition of X iff for A being Subset of X st A in b₂ holds
for V being a_neighborhood of A ex W being Subset of X st
( W is open & A c= W & W c= V & ( for B being Subset of X st B in b₂ & B meets W holds
B c= W ) ) );