## Topology

**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:

**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 defined on arbitrary ...

Spacetime

... Spacetime

**Topology**... Spacetime

**topology**, the topological structure of spacetime, is a subject studied primarily in general relativity ... 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 ...Locally Regular Space - Formal Definition

... has a neighbourhood that is regular under the subspace

... has a neighbourhood that is regular under the subspace

**topology**... if and only if the collection of all open sets that are regular under the subspace**topology**forms a base for the**topology**on X ...Agent Network

... Research in the 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 ... Moreover, agent network**topology**theory is not systematic and relies on graph-based methodology, which is inefficient in describing large-scale agent networks ...**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 ... 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 ...

### More definitions of "topology":

- (
*noun*): The configuration of a communication network.

Synonyms: network topology

- (
*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"*

- (
*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