Boolean functions -- Affine spaces defined by two points -- Morphisms -- Antimorphisms -- Invariant sets -- Invariant subsets -- Path connected set -- Attractors -- The technical condition of proper operation -- The strong technical condition of proper operation -- The generalized technical condition of proper operation -- The strong generalized technical condition of proper operation -- Time-reversal symmetry -- Time-reversal symmetry vs TCPO -- Time-reversal symmetry vs the generalized TCPO.