Cartography
Topographic vs. topological

A topographic map is primarily concerned with the topographic description of a place, including (especially in the 20th and 21st centuries) the use of contour lines showing elevation. Terrain or relief can be shown in a variety of ways (see Cartographic relief depiction). In the present era, one of the most widespread and advanced methods used to form topographic maps is to use computer software to generate digital elevation models which show shaded relief. Before such software existed, cartographers had to draw shaded relief by hand. One cartographer who is respected as a master of hand-drawn shaded relief is the Swiss professor Eduard Imhof whose efforts in hill shading were so influential that his method became used around the world despite it being so labor-intensive.

A topological map is a very general type of map, the kind one might sketch on a napkin. It often disregards scale and detail in the interest of clarity of communicating specific route or relational information. Beck's London Underground map is an iconic example. Although the most widely used map of "The Tube," it preserves little of reality: it varies scale constantly and abruptly, it straightens curved tracks, and it contorts directions. The only topography on it is the River Thames, letting the reader know whether a station is north or south of the river. That and the topology of station order and interchanges between train lines are all that is left of the geographic space. Yet those are all a typical passenger wishes to know, so the map fulfills its purpose.
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