While surfing the web the other day I read an article in which the author refers to a “topological map.” I think it is safe to say that he meant to write “topographic map.” This is an error I’ve seen many times before.
A topographic map is a map of a region that shows changes in elevation, usually with contour lines indicating different fixed elevations. This is a map that you would take on a hike.
A topological map is a continuous function between two topological spaces—not the same thing as a topographic map at all!
I thought for sure that there was no cartographic meaning for topological map. It turns out, however, that there is.
A topological map is a map that is only concerned with relative locations of features on the map, not on exact locations. A famous example is the graph that we use to solve the Bridges of Königsberg problem.
Another famous class of topological maps are subway maps (and other transportation maps in which the vehicles travel along fixed routes). In a subway map, what is most important are the orders of the subway stops on each line and the interconnections between the various subway lines. The map of the London Underground is a well-known topological map.
I’m very happy to learn of this definition. It is a perfect use of the term topological!
(Having said all of this, I still think the author meant topographic map.)