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• Many results of topology involve objects as simple as those mentioned above.
• In some cases, the objects considered in topology are ordinary objects residing in three- (or lower-) dimensional space.
• Topology is a relatively new branch of mathematics; most of the research in topology has been done since 1900.
• This is the oldest branch of topology, and dates back to Euler.
• For the topology of electrical networks, see Topology (electrical circuits) .
• A wide variety of physical topologies have been used in LANs, including ring, bus, mesh and star.
• The transmission medium layout used to link devices is the physical topology of the network.
• For example, the original twisted pair Ethernet using repeater hubs was a logical bus topology carried on a physical star topology.
• The deformations that are considered in topology are homeomorphisms and homotopies.
• The ideas underlying topology go back to Gottfried Leibniz, who in the 17th century envisioned the geometria situs and analysis situs.
• Modern topology depends strongly on the ideas of set theory, developed by Georg Cantor in the later part of the 19th century.
• The term topology also refers to a specific mathematical idea central to the area of mathematics called topology.
• The "objects" of topology are often formally defined as topological spaces.
• Around 1900, Poincaré formulated a measure of an object's topology, called homotopy (Collins 2004).
• There is also a formal definition for a topology defined in terms of set operations.
• This definition can be used to enumerate the topologies on symbols.
• Physicists have typically paid little attention to topology — the mathematical study of shapes and their arrangement in space.
• LISTEN Nature reporters discuss the strange world of topology, and why it’s proving powerful in physics.
• It’s as if each electron contains a tiny Möbius strip that carries a little bit of interesting topology.
• Like the electron’s spin, this topology occurs in an abstract space.
• As a result, symplectic geometry occupies a kind of middle ground between the floppy topology of a tarp and the rigid geometry of a tent.
• To study the quantum hall effect more deeply, physicists turned to a branch of mathematics called topology.
• Perhaps the first work which deserves to be considered as the beginnings of topology is due to Euler .
• He found that the Möbius band could not be filled with compatibly oriented triangles.was the first to use the word topology.
• Listing 's topological ideas were due mainly to Gauss , although Gauss himself chose not to publish any work on topology.
• A second way in which topology developed was through the generalisation of the ideas of convergence.
• The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics.
• Throughout most of its history, topology has been regarded as strictly abstract mathematics, without applications.
• Following the presentation, Robbert Dijkgraaf moderates a panel discussion on topology.
• It is important to note that the first-order and higher-order topologies are not mutually exclusive.
• For topology as a structure on a set, see topological space.
• The key idea of topology is to study spaces with “continuous maps” between them.
• The simple definition of open subsets and the simple principle of continuity gives topology its fundamental and universal flavor.
• ℝ 2 \mathbb{R}^2 , which itself equipped with its standard metric topology (example ).
• Tree network topology -- This topology consists of a parent-child hierarchy in which star networks are interconnected via bus networks.
• Selecting the right topology can improve performance and data efficiency, optimize allocation of resources, and reduce operational costs.
• The modern field of topology draws from a diverse collection of core areas of mathematics.
• Much of basic topology is most profitably described in the language of algebra – groups, rings, modules, and exact sequences.
• Many of these various threads of topology are represented by the faculty at Duke.
• Since its birth in Poincaré's seminal 1894 "Analysis Situs", topology has become a cornerstone of mathematics.
• “Stefan Waldmann’s Topology provides a fast-moving introduction to the core concepts of topology.
• A student well-versed in the notions of set theory and metric spaces should find this an appropriate introductory resource for topology.
• The topology is the branching structure of the tree.
• Rotating any combination of branches around the root always results in the same topology, and thus patterns of relatedness.
• Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them.
• Research of the topology group mainly lies within the areas of homotopy theory and the topology of singular spaces and groupoids.
• The second half of the text includes topics in asymmetric topology, a field motivated by applications in computer science.
• Recurring themes include the interactions of topology with order theory and mathematics designed to model loss-of-resolution situations.
• The configuration, or topology, of a network is key to determining its performance.
• Think of your network as a city, and the topology as the road map.
• The design and structure of a network are usually shown and manipulated in a software-created network topology diagram.
• Even though it’s popular, a ring topology is still vulnerable to failure without proper network management.
• The geometry/topology group has five seminars held weekly during the Fall and Winter terms.
• The Master programme in Topology provides a general background in mathematics, with a special focus on topology and geometry.
• The basic structure of topology is an axiomatic way to make sense of when two points in a set are "near" each other.
• The PostGIS topology module has existed in prior versions of PostGIS but was never part of the Official PostGIS documentation.
• TopologySummary — Takes a topology name and provides summary totals of types of objects in topology.
• This section covers the topology functions for creating new topologies.
• CreateTopology — Creates a new topology schema and registers this new schema in the topology.topology table.
• This page describes recommended topologies for HA VPN.
• HA VPN supports site-to-site VPN in one of the following recommended topologies or configuration scenarios.
• All of these topologies require two VPN tunnels from the perspective of the HA VPN gateway.
• Check with the vendor of your peer VPN gateway to determine which topology is most appropriate.

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