Which of the following is NOT a common element of topology?

Layer visibility is typically associated with the display and management of geographic information in GIS rather than with the foundational concepts of topology. In GIS, topology concerns itself with the spatial relationships between features, such as connectivity, adjacency, and containment. It plays a crucial role in ensuring data integrity and is essential for operations like spatial analysis and network tracing.

Cluster tolerance refers to the distance within which features are considered to be the same, which helps in defining how close spatial features can be to one another without being treated as separate entities. Rules encompass the constraints and relationships that dictate how different geometrical entities interact with each other within a topological model. Ranks can relate to the hierarchy or classification of features based on their topological relationships.

In summary, while layer visibility is important for rendering maps and making data comprehensible to users, it is not a topological principle but rather a practical feature of GIS software aimed at visualization.