To me the most fascinating aspect of prominence is how it identifies the relationships between mountains-- prominence naturally evokes the concept of a 'parent peak', and you can extend that concept to create a global hierarchy of every mountain and hill on earth.
The linked viewer (once you select a mountain) shows the key saddle (lowpoint on path to higher ground), ridgeline, 1st higher ground and parent peak, as well as all child peaks (peaks whose parent is the current peak) ranked by their own prominence.
The demo is limited to North America, but computes all peaks down to a prominence of 20m (about ~2.1M). Only the top 5,000 are indexed on the overview page due to memory constraints of my web server.
Maybe by 0-dimensional you mean that the nodes of the "contour tree" from which prominence can be calculated are labelled with scalars, not vectors. But isosurfaces of a scalar function in an arbitrarily high dimension would still be labelled with scalars. I guess that implies that persistent homology can be used with vector-valued data points to assess the topology of a vector field?
Another CS thing that's somewhat similar in flavour is scale space analysis.
