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topology and was
He introduced the concept of a uniform space in general topology, as a by-product of his collaboration with Nicolas Bourbaki ( of which he was a Founding Father ).
RTMP was the protocol by which routers kept each other informed about the topology of the network.
Felix Hausdorff ( November 8, 1868 – January 26, 1942 ) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, function theory, and functional analysis.
Euler's formula relating the number of edges, vertices, and faces of a convex polyhedron was studied and generalized by Cauchy and L ' Huillier, and is at the origin of topology.
More than one century after Euler's paper on the bridges of Königsberg and while Listing introduced topology, Cayley was led by the study of particular analytical forms arising from differential calculus to study a particular class of graphs, the trees.
He continued to do research on combinatorial topology during a period when England was a major centre of activity notably Cambridge under the leadership of Christopher Zeeman.
The mathematician Leonhard Euler was one of the first to analyze plane mazes mathematically, and in doing so made the first significant contributions to the branch of mathematics known as topology.
Pavel Samuilovich Urysohn, Pavel Uryson () ( February 3, 1898, Odessa – August 17, 1924, Batz-sur-Mer ) was a Jewish mathematician who is best known for his contributions in the theory of dimension, and for developing Urysohn's Metrization Theorem and Urysohn's Lemma, both of which are fundamental results in topology.
The Poincaré conjecture, before being proven, was one of the most important open questions in topology.
At the beginning of the 20th century, Henri Poincaré was working on the foundations of topology — what would later be called combinatorial topology and then algebraic topology.
Since radio circuits inherently possess a broadcast network topology ( i. e., many or all nodes are connected to the network simultaneously ), one of the first technical challenges faced in the implementation of packet radio networks was a means to control access to a shared communications channel.
From about the 1920s onwards, it was realised that tensors play a basic role in algebraic topology ( for example in the Künneth theorem ).
Beck was a London Underground employee who realised that because the railway ran mostly underground, the physical locations of the stations were irrelevant to the traveller wanting to know how to get to one station from another — only the topology of the railway mattered.
An older name for the subject was combinatorial topology, implying an emphasis on how a space X was constructed from simpler ones ( the modern standard tool for such construction is the CW-complex ).
He was a pioneer in the field of low-dimensional topology.
For example, the original twisted pair Ethernet using repeater hubs was a logical bus topology with a physical star topology layout.
In connection with his work on function theory, he was one of the first mathematicians to use the emerging ideas of algebraic topology.
One was devoted to an axiomatic construction of topology via the closure axioms ( Sur la notion de l ' ensemble fini, " Fundamenta Mathematicae ", 1 / 1920 ).
From 1948 to 1980 he was the head of the topology section.
then the topology of above construction only relates to the indeterminate Y, since the topology that was put on has been replaced by the discrete topology when defining the topology of the whole ring.

topology and bus
Although FDDI logical topology is a ring-based token network, it does not use the IEEE 802. 5 token ring protocol as its basis ; instead, its protocol is derived from the IEEE 802. 4 token bus timed token protocol.
FDDI offers both a Dual-Attached Station ( DAS ), counter-rotating token ring topology and a Single-Attached Station ( SAS ), token bus passing ring topology.
: In local area networks where bus topology is used, each node is connected to a single cable.
Since the bus topology consists of only one wire, it is rather inexpensive to implement when compared to other topologies.
:: The type of network topology in which all of the nodes of the network are connected to a common transmission medium which has exactly two endpoints ( this is the ' bus ', which is also commonly referred to as the backbone, or trunk ) – all data that is transmitted between nodes in the network is transmitted over this common transmission medium and is able to be received by all nodes in the network simultaneously.
:: The type of network topology in which all of the nodes of the network are connected to a common transmission medium which has more than two endpoints that are created by adding branches to the main section of the transmission medium – the physical distributed bus topology functions in exactly the same fashion as the physical linear bus topology ( i. e., all nodes share a common transmission medium ).
::# The linear bus topology is sometimes considered to be a special case of the distributed bus topology – i. e., a distributed bus with no branching segments.
::# The physical distributed bus topology is sometimes incorrectly referred to as a physical tree topology – however, although the physical distributed bus topology resembles the physical tree topology, it differs from the physical tree topology in that there is no central node to which any other nodes are connected, since this hierarchical functionality is replaced by the common bus.

topology and cables
The logical topologies are generally determined by network protocols as opposed to being determined by the physical layout of cables, wires, and network devices or by the flow of the electrical signals, although in many cases the paths that the electrical signals take between nodes may closely match the logical flow of data, hence the convention of using the terms logical topology and signal topology interchangeably.
It runs on UTP data or optical fiber cable and uses CSMA / CD in a star wired bus topology, similar to 10BASE-T where all cables are attached to a hub.
Chaosnet's network topology was usually series of linear ( not circular ) cables, each up to a maximum of a kilometer and roughly 12 clients.
In larger installations each band and polarization is given its own cable, so there are 4 cables from the LNB to a switching matrix, which allows the connection of multiple receivers in a star topology using the same signalling method as in a single receiver installation.
How devices are connected to the network through the actual cables that transmit data, or the physical structure of the network, is called the physical topology.
Fibre optic cables connect the headend or hub to optical nodes in a point-to-point or star topology, or in some cases, in a protected ring topology.
A bus network topology is a network architecture in which a set of clients are connected via a shared communications line / cables, called a bus.
Early residential telephone systems used simple screw terminals to join cables to sockets in a tree topology.
This can be achieved by proper routing of the cables, encryption, and a good network topology.

topology and were
Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in 1942 – 45, in connection with algebraic topology.
Functors were first considered in algebraic topology, where algebraic objects ( like the fundamental group ) are associated to topological spaces, and algebraic homomorphisms are associated to continuous maps.
The most valuable results, which were obtained by Kazimierz Kuratowski after the war are those that concern the relationship between topology and analytic functions ( theory ), and also research in the field of cutting Euclidean spaces.
Then S is not a base for any topology on R. To show this, suppose it were.
Prior to this, topological classes in combinatorial topology were not formally considered as abelian groups.
Early in his career, Brouwer proved a number of theorems that were breakthroughs in the emerging field of topology.
Ex hypothesi, the experience of the agent under transformation would change ( as the parts were replaced ), but there would be no change in causal topology and therefore no means whereby the agent could “ notice ” the shift in experience.
Cartan connections were quite rigidly tied to the underlying differential topology of the manifold because of their relationship with Cartan's equivalence method.
The overwhelmingly dominant circuit topology during this period was the single-ended triode gain stage, operating in class A, which gave very good sound ( and reasonable measured distortion performance ) despite extremely simple circuitry with very few components: important at a time when components were hand made and extremely expensive.
At that time ( the beginning of the foundation of general topology ), graphical arguments were still included in proofs, yet were becoming a hindrance to understanding often counter-intuitive results.
The ideas were developed in the period 1955-1965 ( which was roughly the time at which the requirements of algebraic topology were met but those of algebraic geometry were not ).
His main interests were functional analysis and topology: Orlicz spaces are named after him.
In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces ( for example the Betti numbers ) were regarded as derived from combinatorial decompositions such as simplicial complexes.
Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, knot theory and the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry.
To keep this manageable, television equalizer sections were often combined into a single network using ladder topology to form a Cauer equalizer.
Reidemeister's interests were mainly in combinatorial group theory, combinatorial topology, geometric group theory, and the foundations of geometry.
To the British, who were used to fighting in the plains, but were unacquainted with the terrain of the hills, the formidability of the topology is expressed by one anonymous British soldier as such:
Thurston's geometrization conjecture, formulated in the late 1970s, offered a framework that suggested geometry and topology were closely intertwined in low dimensions, and Thurston's proof of geometrization for Haken manifolds utilized a variety of tools from previously only weakly linked areas of mathematics.

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