theorem Th63: :: TOPS_5:63

for I being non empty set
for J being non-Empty TopSpace-yielding ManySortedSet of I
for P being non empty Subset of (product (Carrier J)) st P in FinMeetCl (product_prebasis J) holds
ex I0 being finite Subset of I st
for i being Element of I holds
( (proj (J,i)) .: P is open & ( not i in I0 implies (proj (J,i)) .: P = [#] (J . i) ) )