for T being non empty TopSpace
for F being Subset-Family of T st F is open-domains-family holds
for X being Subset of (Open_Domains_Lattice T) st X = F holds
( ( X <> {} implies "/\" (X,(Open_Domains_Lattice T)) = Int (meet F) ) & ( X = {} implies "/\" (X,(Open_Domains_Lattice T)) = [#] T ) )