Trajectories in topological spaces due to lattice responses for low energies relational processes

The transition from continuous functions ƒ5 to continuous functions ƒ6, both defined on metric spaces, is analyzed. These functions are final responses due to energy variations of processes represented by lattices L50 and L6, respectively. They are algebraically very different: L50 belongs to a nonmodular algebra meanwhile L6 is a pseudo-Boolean algebra belonging to the equational variety H5. A continuous jump function between points defined when ƒ5 ends towards points defined when ƒ6 starts is obtained, and two regions of ending nondistributivity and of starting distributivity come out from .this construction. teractions of these trajectories with the former regions in three-dimensional spaces are studied taking into account energetic considerations. From there it is found how the surface D̄0 of starting distributivity is, which is the energetic gap to reach it from a given constant value, and which is the matter condition for getting the shortest energy way up to get distributivity from a nonmodular process.