topology

Plural: topologies

Noun

• A branch of mathematics dealing with properties of spatial forms.
• topographic study of a given place (especially the history of the place as indicated by its topography)
  • "Greenland's topology has been shaped by the glaciers of the ice age"
• 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
• 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
• 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).
• 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 anatomical structure of part of the body.
• The arrangement of nodes in a communications network.
• The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
• The topographical study of geographic locations or given places in relation to their history.
• The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.

Examples

• A set X equipped with a topology #92;tau is called a topological space and denoted (X,#92;tau).
• The subsets of a set X which constitute a topology are called the open sets of X.
• The ’TOPOLOGY’ of the Scrabble board changes with every word played.

Synonyms

analysis situs, network topology, regional anatomy, topographic anatomy, geometria situs

Related Words

homotopy, topological, topological space, topologically, topologist, toponymy