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Topic: Connected topology


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In the News (Tue 20 Aug 19)

  
  Connected - Wikipedia, the free encyclopedia
In topology, a connected space is a topological space that cannot be partitioned into two open sets.
In geometric topology, a connected sum of two connected m-dimensional manifolds is a manifold formed by deleting an open ball inside each manifold and gluing together the resulting boundary spheres.
In graph theory, a connected graph is a graph in which each pair of vertices is joined by a path.
en.wikipedia.org /wiki/Connected   (246 words)

  
 Network topology - Wikipedia, the free encyclopedia
Network topology is determined only by the configuration of connections between nodes; it is therefore a part of graph theory.
Distances between nodes, physical interconnections, transmission rates, and/or signal types are not a matter of network topology, although they may be affected by it in an actual physical network.
If a link connecting a leaf fails, that leaf is isolated; if a connection to a non-leaf node fails, an entire section of the network becomes isolated from the rest.
en.wikipedia.org /wiki/Network_topology   (1094 words)

  
 Connected sum - Wikipedia, the free encyclopedia
In geometric topology, a connected sum of two connected m-dimensional manifolds is a manifold formed by deleting a ball inside each manifold and gluing together the resulting boundary spheres.
For surfaces, i.e., 2-dimensional manifolds, connected sum with a torus is equivalent to adding a handle.
Every compact surface is the connected sum of one of the sphere, projective plane, or Klein bottle with zero or more tori.
www.wikipedia.org /wiki/Connected_sum   (354 words)

  
 Topology glossary Boundary boundary Category of topological spaces First category Hausdorff homogeneous power set ...   (Site not responding. Last check: 2007-10-21)
Each connected component is closed, and the set of connected components of a space is a partition of that space.
Algebraic topology is the study of topologically invariant abstract algebra constructions on topological spaces.
The weak topology on a set, with respect to a collection of functions from that set into topological spaces, is the coarsest topology on the set which makes all the functions continuous.
en.powerwissen.com /PW9KTznTWeiTenW2ZNJRfA%3D%3D_Partitions_of_unity.html   (4161 words)

  
 Topology
A fully connected topology is a network topology in which there is a direct link between all pairs of nodes.
Bus topology: A network topology in which there is a single line (the bus) to which all nodes are connected and the nodes connect only to this bus.
Star topology: A network topology in which peripheral nodes are connected to a central node, which rebroadcasts all transmissions received from any peripheral node to all peripheral nodes on the network, including the originating node.
www.geocities.com /grade12engineering/topology.htm   (539 words)

  
 Keppanet - Network Basics !   (Site not responding. Last check: 2007-10-21)
All devices are connected to one another in the shape of a closed loop, so that each device is connected directly to two other devices, one on either side of it.
A network topology in which peripheral nodes are connected to a central node, which rebroadcasts all transmissions received from any peripheral node to all peripheral nodes on the network, including the originating node.
A network topology that, from a purely topologic viewpoint, resembles an interconnection of star networks in that individual peripheral nodes are required to transmit to and receive from one other node only, toward a central node, and are not required to act as repeaters or regenerators.
keppanet.netfirms.com /keppanet/supports/networks.htm   (2718 words)

  
 Connected and Path Connected   (Site not responding. Last check: 2007-10-21)
Clearly x is connected to itself, and path connectivity is symmetric and transitive.
Connected and path connected are not equivalent, as shown by the curve sin(1/x) on (0,1] union the origin.
This is a connected half open interval, and its image under the continuous function f is connected.
www.mathreference.com /top,connect.html   (1785 words)

  
 Network topology   (Site not responding. Last check: 2007-10-21)
A network may be represented as a collection of nodes, some of which are connected by links.
Bus topology : A bus topology is a network topology in which there is a single line (the bus) to which all nodes are connected, and the nodes connect only to this bus.
A hybrid topology is a combination of any two or more network topologies in such a way that the resulting network does not have one of the standard forms.
www.sciencedaily.com /encyclopedia/network_topology   (634 words)

  
 Chapter 5: Topology
Physical topology should not be confused with logical topology which is the method used to pass information between workstations.
A star topology is designed with each node (file server, workstations, and peripherals) connected directly to a central network hub or concentrator (See fig.
A star-wired ring topology may appear (externally) to be the same as a star topology.
fcit.usf.edu /network/chap5/chap5.htm   (718 words)

  
 Cartan's Corner : Cartan's Topological Structure I   (Site not responding. Last check: 2007-10-21)
Recall that a topology is a method of determining a topological structure, whose utility is in giving a definition to what is meant by continuous.
As it is impossible to construct a continuous map from a connected to a disconnected topology, it follows that a transition from a laminar flow (A^dA=0) to a turbulent flow (A^dA>0) must be a discontinuous process.
On the other hand, a continous map from a disconnected topology to a connected topology is possible, therefor the decay of turbulence can be studied in terms of continuous processes.
www22.pair.com /csdc/car/carfre28.htm   (230 words)

  
 Webopedia: Network Topologies
Topology refers to the shape of a network, or the network's layout.
All devices are connected to a central hub.
All devices are connected to a central cable, called the bus or backbone.
www.webopedia.com /quick_ref/topologies.asp   (160 words)

  
 Connectedness
R with its usual topology is not connected since the sets [0, 1] and [2, 3] are both open in the subspace topology.
The spaces [0, 1] and (0, 1) (both with the subspace topology as subsets of R) are not homeomorphic.
[2, 3] with the subspace topology inherited from R, are the subspaces [0, 1] and [2, 3].
www-groups.dcs.st-and.ac.uk /~john/MT4522/Lectures/L19.html   (619 words)

  
 Simply Connected   (Site not responding. Last check: 2007-10-21)
A topological space is simply connected if it is path connected, and it has no holes.
Formally,any two paths connecting a and b can be continuously "moved" towards each other, until they coincide.
Unless otherwise stated, simply connected refers to paths and circles, regardless of the dimension of the containing space.
www.mathreference.com /top,sconnect.html   (213 words)

  
 Assesing Network Needds
network topology: The specific physical, i.e., real, or logical, i.e., virtual, arrangement of the elements of a network.: Two networks have the same topology if the connection configuration is the same, although the networks may differ in physical interconnections, distances between nodes, transmission rates, and/or signal types.
Instances can occur where two basic network topologies, when connected together, can still retain the basic network character, and therefore not be a hybrid network.
ยท tree topology: A network topology that, from a purely topologic viewpoint, resembles an interconnection of star networks in that individual peripheral nodes are required to transmit to and receive from one other node only, toward a central node, and are not required to act as repeaters or regenerators.
www.angelfire.com /tx/psemar/Topology.html   (1197 words)

  
 topology - a Whatis.com definition
In communication networks, a topology is a usually schematic description of the arrangement of a network, including its nodes and connecting lines.
In the star network topology, there is a central computer or server to which all the workstations are directly connected.
In the ring network topology, the workstations are connected in a closed loop configuration.
searchnetworking.techtarget.com /sDefinition/0,,sid7_gci213156,00.html   (415 words)

  
 Vector » Handbook of Neural Computation (Ed. Emile Fiesler et al) » Fully connected topologies   (Site not responding. Last check: 2007-10-21)
The simplest topologies are the fully connected ones, where all possible connections are present.
The most commonly used topology is the fully interlayer-connected one, where all possible interlayer connections are present but no intra- or supralayer ones.
A slightly more popular 'fully connected' topology is a plenary neural network without self-connections, as used for example for some associative memories.
dx.doi.org /10.1887/0750303123/b365c17   (154 words)

  
 CIS 321 - Wednesday January 10   (Site not responding. Last check: 2007-10-21)
If you wanted to place a call you had to connect your phone to the correct wire and hope the person you wished to speak was also connected to it.
The connection strategy which is used in a network is known as a network topology.
When a network uses a common bus topology each machine or node on the network is connected to a simple bus (a connection of parallel lines).
www.cis.usouthal.edu /~lynn/spring2001/documents/jan10.html   (2010 words)

  
 What Is A Network? - Computer Networks
The topology of a network specifies the geometric arrangement of the network or a description of the layout of a specific region or area covered by a network.
Bus topology is a passive topology, which means that computers connected to a bus topology only listen for a signal being transmitted over the data-transmission media.
Ring topology is an active topology, which means that computers connected to a ring topology are responsible for moving data from themselves to the next computer.
www.bellaonline.com /ArticlesP/art1057.asp   (1649 words)

  
 Computer Support News Bulletins
All fiber feeds are connected to one central switch (the backbone of the star topology); the speed of this switch is currently 1 GB/s (scheduled to be upgraded).
The backbone of the star topology is connected to SONNET (the OSU campus network) through the departmental firewall.
Each jack is individually connected to the hub or switch on your floor and allows you to use the entire bandwidth of that connection (10 or 100 MB/s, depending on the hub or switch on your floor).
www.chem.osu.edu /compsupp/Bulletin/2000-09-11.html   (579 words)

  
 What is topology? - A Word Definition From the Webopedia Computer Dictionary   (Site not responding. Last check: 2007-10-21)
bus topology: All devices are connected to a central cable, called the bus or backbone.
ring topology : All devices are connected to one another in the shape of a closed loop, so that each device is connected directly to two other devices, one on either side of it.
Ring topologies are relatively expensive and difficult to install, but they offer high bandwidth and can span large distances.
www.webopedia.com /TERM/T/topology.html   (237 words)

  
 Network Topologies
Topology refers to the way in which the network of computers is connected.
Each topology is suited to specific tasks and has its own advantages and disadvantages.
One of these ports is connected to a server, or the output of the hub can be connected to other hubs.
physinfo.ulb.ac.be /cit_courseware/networks/pt2_1.htm   (653 words)

  
 topologies   (Site not responding. Last check: 2007-10-21)
he main advantages of the star topology is the each node is independent from the rest, i.e.
ach node is connected just like a circle of people holding the hand of the person on either side, thus creating a ring or loop.
The main advantages of the ring topology is that no dependence on central host.
www.scit.wlv.ac.uk /~c9711026/topologies.html   (288 words)

  
 Covering map Examples continuous homeomorphism unit circle bijection property Riemann surface permutes normal subgroup ...   (Site not responding. Last check: 2007-10-21)
If X is simply connected, then this holds globally as well, and the covering p is a homeomorphism.
On every connected component of X, the cardinality of the fibers is the same (possibly infinite).
If x and y are two points in X connected by a path, then that path furnishes a bijection between the fiber over x and the fiber over y via the lifting property.
en.powerwissen.com /o0T%2BDihhwOfvZQrOn%2BDpwQ%3D%3D_Covering_map.html   (1642 words)

  
 Connected space : Locally connected   (Site not responding. Last check: 2007-10-21)
Equivalently, it can't be divided into two disjoint nonempty closed sets (since the complement of an open set is closed).
Some authorities accept the empty set (with its unique topology) as a connected space, while others do not.
The maximal[?] nonempty connected subsets of any topological space are called the components of the space.
www.termsdefined.net /lo/locally-connected.html   (605 words)

  
 Definition: network topology   (Site not responding. Last check: 2007-10-21)
bus topology: A network topology in which all nodes, i.e., stations, are connected together by a single bus.
fully connected topology: A network topology in which there is a direct path (branch) between any two nodes.
tree topology: A network topology that, from a purely topologic viewpoint, resembles an interconnection of star networks in that individual peripheral nodes are required to transmit to and receive from one other node only, toward a central node, and are not required to act as repeaters or regenerators.
www.its.bldrdoc.gov /fs-1037/dir-024/_3535.htm   (547 words)

  
 Topology Of Two-Connected Graphs And Homology Of Spaces Of Knots - Vassiliev (ResearchIndex)
More generally, for any finite-order cohomology class of the space of knots we define its principal symbol, which lies in a cohomology group of a certain finitedimensional...
Topology of Matching, Chessboard, and General Bounded Degree Graph..
V.A. Vassiliev, Topology of two-connected graphs and homology of spaces of knots, Di#erential and symplectic topology of knots and curves, 253--286, Amer.
citeseer.ist.psu.edu /vassiliev97topology.html   (410 words)

  
 [No title]   (Site not responding. Last check: 2007-10-21)
Definitions: Connected -- not the union of two disjoint nonempty open subsets Arcwise connected -- for any two points a, b there is a continuous f : [0,1] -> X with f(0)=a, f(1)=b Theorem: X arcwise connected => X connected Example: converse does not hold.
"Arcwise connected" is the property that's more related to the drawing of pictures, which perhaps makes it more appropriate for geometry.
On the other hand, you can't expect the stronger results to apply in general, and you may have a hard time coming up with "internal" properties of a topological space (Hausdorff, first countable, etc.) which would allow you to draw the desired conclusions.
www.math.niu.edu /~rusin/known-math/99/topo101   (304 words)

  
 1   (Site not responding. Last check: 2007-10-21)
If computers are connected in a row, along a single cable this is called a bus topology, if they branch out from a single junction or hub this is known as a star topology.
In bus topologies, all computers are connected to a single cable or "trunk or backbone", by a transceiver either directly or by using a short drop cable.
In a ring topology network computers are connected by a single loop of cable, the data signals travel around the loop in one direction, passing through each computer.
www.toggit.com /NetPlus/more/NetPlus.htm   (10355 words)

  
 concepts chapter 6 page   (Site not responding. Last check: 2007-10-21)
The physical media used to connect the networks are: Twisted pair, coaxial cable, fiber optic cable, and space.
Can be as small as connecting two computers together to as large as the largest of all, the Internet.
The nodes are linked in a bus, ring, star, tree, or fully connected topology network configuration.
www.casc.cc.ok.us /~smith/computerconcepts/conchap6.htm   (1310 words)

  
 Topology of the Universe
Suppose instead that there is this continuous multiply connected 3D spatial topology of a hyper N torus.
Star Gates that physically implement the formal global multiply connected topology in which the 12 2D pentagon "walls" of the spherical dodecahedron have 3D "handles" connecting them into what I imagine are 6 pairs of opposite walls that are The Doors in and out either way so to speak.
The manifold is an abstract space in void with appropriate topology and metric.
www.usenet.com /newsgroups/sci.astro/msg03586.html   (2579 words)

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