BOOLEAN [0,1]-VALUED CONTINUOUS OPERATORS

We prove the following claim. THEOREM There are continuous operators , perpendicular to, # on [0,1] such that ([0,1], , perpendicular to, #) approximate a Boolean algebraic structure on [0,1] for an arbitrary preciseness. square In other words, for any epsilon > 0, We can conti nuous functionally define a Boolean algebraic structure on [0, 1] modu le epsilon. Here, the meaning of ''modulo epsilon'' is the following. We can take points {r(1),...,r(2n)} in [0,1] such that max{(r(i+1)-r(i ))\0 less than or equal to i less than or equal to 2(n)-1}<epsilon, so that ({r(1),...,r(2n)}, , perpendicular to, #) becomes a Boolean alg ebra.