What is topology?

  • (noun): 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.
    Synonyms: analysis situs
    See also — Additional definitions below


Topology (from the Greek τόπος, “place”, and λόγος, “study”) is a major area of mathematics concerned with the most basic properties of space, such as connectedness. More precisely, topology studies properties that are preserved under continuous deformations, including stretching and bending, but not tearing or gluing. The exact mathematical definition is given below. Topology developed as a field of study out of geometry and set theory, through analysis of such concepts as space, dimension, and transformation.

Read more about Topology.

Some articles on topology:

Spacetime Topology
... Spacetime topology, the topological structure of spacetime, is a subject studied primarily in general relativity ... physical theory models gravitation as a Lorentzian manifold (a spacetime) and the concepts of topology thus become important in analysing local as well as global aspects of spacetime ... The study of spacetime topology is especially important in physical cosmology ...
Topology Control
... Topology control is a technique used in distributed computing to alter the underlying network (modeled as a graph) in order to reduce the cost of distributed algorithms if ran over the new resulting ... The term "topology control" is consumed mostly by the wireless ad hoc and sensor networks research community ... The main aim of topology control in this domain is to save energy, reduce interference between nodes and extend lifetime of the network ...
Topology Topics - Generalizations
... Occasionally, one needs to use the tools of topology but a "set of points" is not available ... In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures ...
Agent Network Topology
... Research in the agent network topology area adopts topological theory from the distributed system and computing network fields, such as local area network (LAN) without considering mobility ... Moreover, agent network topology theory is not systematic and relies on graph-based methodology, which is inefficient in describing large-scale agent networks ...
Locally Regular Space - Formal Definition
... x, of X has a neighbourhood that is regular under the subspace topology ... if the collection of all open sets that are regular under the subspace topology forms a base for the topology on X ...

More definitions of "topology":

  • (noun): The configuration of a communication network.
    Synonyms: network topology
  • (noun): 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.
    Synonyms: regional anatomy, topographic anatomy
  • (noun): Topographic study of a given place (especially the history of place as indicated by its topography).
    Example: "Greenland's topology has been shaped by the glaciers of the ice age"