Conjugate topology of pointwise metric molecular lattices

In this paper the pointwise pseudo-metric for molecular lattices introduced by Shi is studied. A series of expressions concerning neighborhood balls and remote-neighborhood balls are obtained. Some algebraic properties of the pointwise pseudo-metric function of molecular lattices are presented and their topological structure are discussed in terms of the conjugate families of mappings. These results show that there exist conjugate relations between neighborhoods and remote-neighborhoods.