A branch of mathematics studying those properties of a geometric figure or solid that are not changed by stretching, bending and similar homeomorphisms
A collection τ of subsets of a set X such that the empty set and X are both members of τ and τ is closed under arbitrary unions and finite intersections
The study of how geometric objects are intrinsically connected to themselves Since topologists are not concerned with the geometric measurements of objects, people often say that they study objects up to continuous deformation But usually topologists consider spaces which have a topology (a qualitative shape or connectivity) but no predefined (quantitative) geometry Knots and manifolds are typical examples of topological spaces
the configuration of a communication network 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 topographic study of a given place (especially the history of place as indicated by its topography); "Greenland's topology has been shaped by the glaciers of the ice age
Topology is the structure of the network, including physical connections such as wiring schemes and logical interactions between network devices
topographic study of a given place (especially the history of place as indicated by its topography); "Greenland's topology has been shaped by the glaciers of the ice age"
In mathematics, the study of the properties of a geometric object that remains unchanged by deformations such as bending, stretching, or squeezing but not breaking. A sphere is topologically equivalent to a cube because, without breaking them, each can be deformed into the other as if they were made of modeling clay. A sphere is not equivalent to a doughnut, because the former would have to be broken to put a hole in it. Topological concepts and methods underlie much of modern mathematics, and the topological approach has clarified very basic structural concepts in many of its branches. See also algebraic topology
The physical layout of network components (cable, stations, gateways, hubs and so on) There are three basic interconnection topologies?star, ring and bus networks
The relative location of geographic phenomena independent of their exact position In digital data, topological relationships such as connectivity, adjacency and relative position are usually expressed as relationships between nodes, links and polygons For example, the topology of a line includes its from- and to-nodes, and its left and right polygons Topology is useful in GIS because many spatial modelling operations don not require coordinates, only topological information For example, to find an optimal path between two points requires a list of the lines or arcs that connect to each other and the cost to traverse each line in each direction Coordinates are only needed for drawing the path after it is calculated
Topology is the map, or visual layout of the frame relay network Frame relay network topology must be viewed from several perspectives to fully understand the network and the equipment used to construct the network Topological views include an overview map, a logical connection map, perhaps a functional map, a map showing the detail equipment and channel links, an address map
There are two types of topology: physical and logical The physical topology of a network refers to the configuration of cables, computers, and other peripherals Logical topology is the method used to pass the information between workstations Issues involving logical topologies are discussed on the Protocol chapter
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
Term used to describe a general characteristic of a LAN technology which more or less describes the shape of the necessary wiring Three examples are bus, ring, and star
As in network topology The geometric physical or electrical configuration describing a local communication net-work; the shape or arrangement of a system The most common topologies are the bus, ring and star
The physical or logical layout of links and nodes in a network These include star, ring and bus configurations
The spatial relationships between connecting or adjacent coverage features (e g , arcs, nodes, polygons, and points) For example, the topology of an arc includes its from- and to-nodes, and its left and right polygons Topological relationships are built from simple elements into complex elements: points (simplest elements), arcs (sets of connected points), areas (sets of connected arcs), and routes (sets of sections, which are arcs or portions of arcs) Redundant data (coordinates) are eliminated because an arc may represent a linear feature, part of the boundary of an area feature, or both Topology is useful in GIS because many spatial modeling operations don't require coordinates, only topological information For example, to find an optimal path between two points requires a list of the arcs that connect to each other and the cost to traverse each arc in each direction Coordinates are only needed for drawing the path after it is calculated
In communications, the physical or logical arrangement of nodes in a network, especially the relationships among nodes and the links between them
The arrangement of nodes that comprise the network Types include star, ring, bus, and tree
Can be either physical or logical Physical topology describes the physical connections of a network and the geometric arrangement of links and nodes that make up that network Logical topology describes the possible logical connections between nodes, and indicates which pairs of nodes are able to communicate
A network topology shows the computers and the links between them A network layer must stay abreast of the current network topology to be able to route packets to their final destination
The map or plan of the network The physical topology describes how the wires or cables are laid out, and the logical or electrical topology describes how the information flows
{i} non-quantitative geometry, branch of mathematics dealing with geometric configurations that remain unchanged by stretching bending or twisting (Mathematics)
A program that displays the topology of a Marconi ATM network An updated topology can be periodically re-displayed by use of the interval command option
The physical layout of a network The principal LAN topologies are bus, ring, and star
A collection of subsets of a topological space closed under the operations of union and intersection
A network topology in which, in the physical case, every node of a network is connected to exactly two other nodes: one node designated as upstream and the other as downstream. A given node receives data from its upstream node and sends data to its downstream node
Field of mathematics that uses algebraic structures to study transformations of geometric objects. It uses functions (often called maps in this context) to represent continuous transformations (see topology). Taken together, a set of maps and objects may form an algebraic group, which can be analyzed by group-theory methods. A well-known topic in algebraic topology is the four-colour map problem