Difference Between Topology and Topography

Key Difference – Topology vs Topography
 

Topology and topography are two words that are commonly misused by many English speakers. Although these two words sound alike, they have very different meanings. Topology is concerned with the geometrical properties and spatial relations that are unaffected by the continuous change of shape or size of figures. Topography is concerned with the arrangement of the natural and artificial physical features of an area. The key difference between topology and topography is that topology is a field in mathematics whereas topography is a field in geography.

What is Topology?

Topology is a branch in mathematics which is concerned with the properties of space that are unaffected by elastic deformations such as stretching or twisting. For example, a circle is topologically equivalent to an ellipse since it can be deformed by stretching. It is also concerned with the study of spatial features such as surfaces, curves, and the space that is called the universe.

This branch in mathematics was developed from geometry and set theory, through the analysis of concepts such as space, dimensions, and transformations. Leonhard Euler’s 1736 paper on the Seven Bridges of Königsberg is considered as one of the first practical applications of topology.

Topology also has many subfields such as algebraic topology, general topology, differential topology, and geometrical topology.

The Seven Bridges of Königsberg: 

The old town of Königsberg has seven bridges. How can you walk through the town, visiting each part of the town
and crossing each bridge only once?

What is Topography?

Topography is a branch of geography, which is concerned with the study of surface features of the Earth and other observable astronomical objects such as sun, moon, and planets.  The phrase topography of an area refers to the natural and artificial physical features of an area.

The main purpose of topography is to identify specific features of an area, recognize typical landform patterns, and to determine the position of any feature using latitudes, longitudes, and altitudes.

In a narrow sense, topography only includes relief or terrain, specific landforms and three-dimensional surface of the area. A topographic map is a map that shows the above features. Such features are represented on a map using a variety of techniques including relief shading, contour lines, and hypsometric tints. Given below is an example of a topographical map.

What is the difference between Topology and Topography?

Field:

Topology is a field of mathematics.

Topography is a field of geography.

Definition:

Topology is the study of geometrical properties and spatial relations unaffected by the continuous change of shape or size of figures.

Topography is the study of the arrangement of the natural and artificial physical features of an area.

Map:

Topology does not generally use map.

Topography often uses map.

Image Courtesy: 

“Konigsberg bridges” By Bogdan Giuşcă –  based on a Public Domain image (CC BY-SA 3.0) via Commons Wikimedia

“R.o.Macedonia topography” By Future Perfect at Sunrise – Own work (Public Domain) via CommonsWikimedia

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