Functional equations in total negation

Abstract

AbstractIt is known that the only topological invariants P for which anti(P) = anti2 (P), anti( ) denoting Bankston's total negation operator, are those which are determined purely by the cardinality of the underlying point-set. We examine equations of the form antin (P) = antin (not P), reaching similar conclusions for n ≤ 2 but weaker ones for n > 3. A corresponding investigation for total negation within a constraint is initiated.