Topology vs. Topography — What's the Difference?

Focuses on abstract spatial properties.

Used in cartography and surveying.

Applicable to network design in computer science.

The study of Earth's surface features.

Concerned with properties unaffected by continuous transformations.

Maps physical features relative to each other.

In mathematics, topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity.

Topography is the study of the forms and features of land surfaces. The topography of an area could refer to the surface forms and features themselves, or a description (especially their depiction in maps).

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

The arrangement of the natural and artificial physical features of an area

The way in which constituent parts are interrelated or arranged

The distribution of parts or features on the surface of or within an organ or organism.

Topographic study of a given place, especially the history of a region as indicated by its topography.

Detailed, precise description of a place or region.

(Medicine) The anatomical structure of a specific area or part of the body.

Graphic representation of the surface features of a place or region on a map, indicating their relative positions and elevations.

The study of certain properties that do not change as geometric figures or spaces undergo continuous deformation. These properties include openness, nearness, connectedness, and continuity.

A description or an analysis of a structured entity, showing the relations among its components

The underlying structure that gives rise to such properties for a given figure or space

The surface features of a place or region.

(Computers) The arrangement in which the nodes of a network are connected to each other.

The surface features of an object

The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing).

The surveying of the features of a place or region.

(topology) Any collection τ of subsets of a given set X that contains both the empty set and X, and which is closed under finitary intersections and arbitrary unions.

The study or description of an anatomical region or part.

(medicine) The anatomical structure of part of the body.

A precise description of a place.

(computing) The arrangement of nodes in a communications network.

A detailed graphic representation of the surface features of a place or object.

(technology) The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.

The features themselves; terrain.

(topography) The topographical study of geographic locations or given places in relation to their history.

The surveying of the features.

(dated) The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.

(by extension) A figurative landscape; a structure of interrelated ideas, etc.

The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.

The description of a particular place, town, manor, parish, or tract of land; especially, the exact and scientific delineation and description in minute detail of any place or region.

A branch of mathematics which studies the properties of geometrical forms which retain their identity under certain transformations, such as stretching or twisting, which are homeomorphic. See also topologist.

The configuration of a surface and the relations among its man-made and natural features

Configuration, especially in three dimensions; - used, e. g. of the configurations taken by macromolecules, such as superhelical DNA.

Precise detailed study of the surface features of a region

Topographic study of a given place (especially the history of place as indicated by its topography);

Concerned with elevations and depressions.

The study of anatomy based on regions or divisions of the body and emphasizing the relations between various structures (muscles and nerves and arteries etc.) in that region

Involves empirical methods and observation.

The branch of pure mathematics that deals only with the properties of a figure X that hold for every figure into which X can be transformed with a one-to-one correspondence that is continuous in both directions

The configuration of a communication network

A branch of mathematics studying spatial relations.

Can be theoretical or practical.