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Topic: Base (topology)

	Base (topology) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-05)
		In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B.
		Bases are useful because many properties of topologies can be reduced to statements about a base generating that topology, and because many topologies are most easily defined in terms of a base which generates them.
		The metric topology is usually defined as the topology generated by a collection of open balls.
	en.wikipedia.org /wiki/Base_(topology) (803 words)

	Wikinfo \| Base
		In topology, a base (topology) for a topology is a set of open sets such that every element of the topology is a union of the base sets.
		In baseball, a base is one of 4 bags placed at corners of the infield diamond that a player has to run to after hitting the ball.
		Base is also an isolated settlement in inhospitable conditions that must rely on outide help in order to survive, such as military base, Antarctica base, Moon base.
	www.wikinfo.org /wiki.php?title=Base (334 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		Other known connection topologies include the tree topology, in which a trunk line starting from the base station controller branches from a base transceiver station to another, and the ring topology in which the base transceiver stations and the base station controller are interconnected so as to form a ring-like system.
		Base transceiver stations 301,302,303 and 304 are connected into a ring by means of a known transmission system 305 proper, which may be e.
		A base station subsystem according to claim 9, characterized in that it com- prises in at least one base transceiver station and in the base station controller an ISDN basic-rate interface (204).
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=99/45727.990910&ELEMENT_SET=DECL (2475 words)

	PlanetMath: basis (topology)
		A basis for the usual topology of the real line is given by the set of open intervals since every open set can be expressed as a union of open intervals.
		More generally, the set of open balls forms a basis for the topology on a metric space.
		This is version 11 of basis (topology), born on 2002-01-01, modified 2004-12-20.
	planetmath.org /encyclopedia/Base2.html (327 words)

	A Base for the Topology (Site not responding. Last check: 2007-11-05)
		If the base criterion fails, then x∩y cannot be a union of base sets, and is not open; yet it must be open, as it is the intersection of two open sets.
		The finite intersection of base sets is thus a union of base sets, and is open, as it should be.
		The union of all these base sets z is the finite intersection of our original open sets, hence the finite intersection of open sets is open, and the base generates a valid topology.
	www.mathreference.com /top,base.html (498 words)

	ECN Asia : Electronic Component & Product Information (Site not responding. Last check: 2007-11-05)
		The choice of the appropriate short-range mesh topology depends on the amount and frequency of the data to be transmitted, transmission distance, battery life requirements and the mobility and level of change in the sensor or device nodes.
		A star topology is a single-hop system in which all wireless sensor nodes are within direct communication range (usually 30 to 100 meters) to a base (monitoring) station.
		Mesh topologies are multi-hopping systems in which all wireless sensor nodes are identical and communicate with each other to hop data to and from the sensor nodes and base station.
	www.ecnasiamag.com /print.asp?id=2156 (1110 words)

	[No title]
		Topology Glossary Mainly extracted from (a) UC Davis Math:Profile Glossary (http://www.math.ucdavis.edu/profiles/glossary.html) by Greg Kuperberg (http://www.math.ucdavis.edu/profiles/kuperberg.html), and (b) Topology Atlas Glossary (http://www.achilles.net/~mtalbot/TopoGloss.html).
		An early result in topology states that every closed 3-manifold (closed meaning that the manifold is finite and connected but has no boundary) has a Heegaard splitting and a resulting description in terms of a Heegaard diagram, which describes how the two handlebodies are glued together.
		In 3-dimensional topology, a surface in a 3-manifold with the property that no essential circle in the surface bounds a disk in the manifold.
	www.ornl.gov /sci/ortep/topology/defs.txt (5717 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		A base transceiver station according to the invention is characterized in that it com- prises means for routing information transferred between a base transceiver station and base station controller through the air interface.
		Base transceiver stations 201 and 203 are linked 204,205 in a fixed manner with the base station controller 200 but the link 206 between base transceiver station 202 and base station controller 200 only exists when needed, which is why it is depicted by a dashed line in the figure.
		Similarly, uplink data sent by the control block in base transceiver station 202 are transmitted by a transmitter block in base transceiver station 202 in the uplink portion of said traffic channel and received at the link BTS 201 and directed to the base station controller 200.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=99/45728.990910&ELEMENT_SET=DECL (3144 words)

	Base - Voyager, the free encyclopedia (Site not responding. Last check: 2007-11-05)
		base is a political party's core group of voters.
		In warfare, a military base is a logistics point such as a supply dump and a concentrated facility for storing and repairing military equipment such as an air force base.
		In architecture, a base is the part of a column between the bottom of the shaft and the top of the pedestal.
	www.voyager.in /Base (532 words)

	DNA Structure and Topology
		Each nucleotide base of one strand is paired with a nucleotide base on the other strand to create a stable structure of the two polymers.
		Since the bases are attached to the sugars, and each base is paired to its complementary base, the edges of the bases are exposed to solvent within two grooves along the helix, the "major groove" and the "minor groove".
		Topology is the branch of mathematics that studies properties of objects that are invariant to continuous deformations of the object.
	www.rpi.edu /~bellos/new_page_1.htm (5130 words)

	Tutorial for the UCB/LBNL/VINT Network Simulator "ns"
		In this section we are going to extend the simple wireless topology created in section IX to create a mixed scenario consisting of a wireless and a wired domain, where data is exchanged between the mobile and non-mobile nodes.
		Base station nodes are like gateways between wireless and wired domains and allow packets to be exchanged between the two types of nodes.
		Based on the registration/beacons exchanged between the MH and the base-station node (of the domain the MH is currently in), the base-station's address is assigned as the MH's COA.
	www.isi.edu /nsnam/ns/tutorial/nsscript6.html (2421 words)

	.:: SkyPilot \| Technology ::. (Site not responding. Last check: 2007-11-05)
		The base station in a point-to-multipoint network is simply unable to extend coverage to reach prospective subscribers that lie outside its range.
		This issue is compounded by the inflexibility of the topology to add base stations closer to the subscribers to increase modulation without also causing interference.
		Since the base station is a single device serving its entire coverage area, any disruption to it affects all of its subscribers.
	www.skypilot.com /technology/p2mp.htm (318 words)

	[No title]
		The county files have a coverage area based on the legal boundaries obtained in response to the U.S. Census Bureau's Census 2000 Boundary and Annexation Survey (BAS).
		Topology and Spatial Objects in the TIGER/Line Files Spatial Objects in the TIGER/Line Files The Census TIGER data base uses a collection of spatial objects, points, lines, and polygons, to model or describe real-world geography.
		Topology Topology explains how points, lines, and areas relate to each other and is used as the foundation for organizing spatial objects in the Census TIGER data base.
	www.census.gov /geo/www/tiger/tiger2k/a2kch1.txt (4106 words)

	Math Forum: Leonard Euler and the Bridges of Konigsberg
		Topology is one of the newest branches of mathematics.
		The foundations of topology are often not part of high school math curricula, and thus for many it sounds strange and intimidating.
		However, there are some readily graspable ideas at the base of topology that are interesting, fun, and highly applicable to all sorts of situations.
	mathforum.org /isaac/problems/bridges1.html (336 words)

	A Local Base for the Topology (Site not responding. Last check: 2007-11-05)
		Let's show that b is a base for a given topology iff it includes a base at p for every point p.
		Given the former, place p in an arbitrary open set w, which is the union of base sets, hence p is contained in a base open set inside w.
		If p is in the intersection of base open sets, p is contained in a base open set that is contained in the intersection, and that takes care of the base criterion.
	www.mathreference.com /top,lbase.html (161 words)

	PlanetMath: pseudometric topology
		Therefore, we have, in fact, also shown that any quasimetric induces a topology.
		Cross-references: symmetric, triangle inequality, cover, pseudometric, induced, topology, base, collection, metric space, pseudometric space
		This is version 3 of pseudometric topology, born on 2004-10-03, modified 2004-10-27.
	planetmath.org /encyclopedia/PseudometricTopology.html (133 words)

	The Network Simulator ns-2: Topology Generation
		Download the Inet Topology Generator from University of Michigan and create a internet topology using the configuration parameter.
		Use inet2ns to convert the inet topology to ns.
		The GT-ITM topology generator can be used to create flat random graphs and two types of hierarchical graphs, the N-level and transit-stub.
	www.isi.edu /nsnam/ns/ns-topogen.html#tiers (576 words)

	Topology Security for Network Media
		While increasing the level of topology security may appear to be an expensive proposition, the cost may be more than justified when compared to the cost of recovering from an intrusion.
		Topology is defined as the rules for physically connecting and communicating on given network media.
		Unlike a bridge, which will handle any valid topology traffic you throw at it, a router has to be specifically designed to support both the topology and the protocol being used.
	www.microsoft.com /technet/security/topics/networksecurity/topology.mspx (9760 words)

	10 Base-T Basics
		Both systems provided a network with excellent performance, but they utilized a bus topology which made changing a network a difficult proposition, and also left much to be desired in regard to reliability.
		Each node on the network has its own cable run back to a common hub, and each of these cable runs may be up to 100 meters (330 feet) in length.
		Because of the partitioning function built in to the hubs and the star-wired topology, it is generally easy to troubleshoot a 10 Base-T network.
	www.ictp.trieste.it /~radionet/ghana1998/CABLING/10BASET.HTM (815 words)

	[No title]
		All changes to the base would have to be mirrored in the derived, which would require all code that modifies the base, including user-written code in actors, to mirror the changes in all derived classes.
		One possibility would be to prohibit changes in the base topology after a derived topology is created.
		If the derived topology changes after cloning, as in the above example, and these changes involve only addition to the topology (new entities, ports, relations, or links) or changes to parameter values, then in principle it would not be difficult to generate those additions in the MoML body.
	ptolemy.eecs.berkeley.edu /projects/hmad/reports/99/12 (2160 words)

	EECS 845 - Implementation of High-Performance Integrated Networks (Site not responding. Last check: 2007-11-05)
		It should be noted that floodgated neighbors (neighbors which have a floodgated interface between them) should always be reachable across the base topology.
		Those neighbors which are reachable across the area's base topology and from whom acknowledged floodgate type LSAs have been received with matching floodgate type are listed in the LSAs opaque data.
		When the local router finds that the floodgated neighbor is unreachable across the base topology, an OpenFloodgate Event is generated and the floodgate is opened and state reaches Inactive.
	www.ittc.ku.edu /~sandeeps/ospf.html (629 words)

	DNA Structure/Topology (Site not responding. Last check: 2007-11-05)
		The bases are not simply nonpolar, such as the alkyl chains of amino acids or lipids, or the phenyl rings of Phe, Tyr.
		In general, stacking interactions with a GC base pair are stronger than those with an AT bp.
		That is because it is difficult for the first few bases to dis-engage from the duplex.
	svik.life.smu.edu /5310/5310lectures/lect24.html (840 words)

	Topology Course Lecture Notes
		The discrete topology for X is the finest one; the trivial topology is the coarsest.
		That form of definition is useless in the absence of a properly defined 'distance' function but, fortunately, it is equivalent to the demand that the preimage of each open subset of the target metric space shall be open in the domain.
		We learnt that, for metric spaces, sequential convergence was adequate to describe the topology of such spaces (in the sense that the basic primitives of `open set', `neighbourhood', `closure' etc. could be fully characterised in terms of sequential convergence).
	at.yorku.ca /i/a/a/b/23.dir/ch1.htm (2430 words)

	LWN: Patch: Core sysfs Topology 2.5.45 (1/5)
		(1/5) Core sysfs Topology: This patch creates the generic structures that are (will be) embedded in the per-arch structures.
		This is used by driverFS topology to keep track of which memory blocks are in the system and online.
		This is used by driverFS topology to keep track of which Nodes are in the system and online.
	lwn.net /Articles/14287 (521 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		The geographic coverage for a single TIGER/Line file is a county or statistical equivalent entity, with the coverage area based on January 1, 1995 legal boundaries.
		TIGER/Line files are extracted from the Census TIGER data base by county or statistical equivalent area.
		Topology explains how points, lines, and areas relate to each other and is used as the foundation for organizing spatial objects in the Census TIGER data base.
	www.geo.ed.ac.uk /~anp/linktest/ptiger.txt (2533 words)

	ASAP '95 On Optimizing Base Station Antenna Array Topology for Coverage Extension in Cellular Radio ... (Site not responding. Last check: 2007-11-05)
		Also, since the forward link (base station to mobile) has higher power than the reverse link, coverage is limited by the reverse link.
		When receive antenna arrays are used at the base station, the array design parameters affect several aspects of the system performance and cost.
		In this presentation, we study performance of linear and circular base station antenna arrays with grouped vs uniform topology as a function of angle spread, number of elements used, and maximum array span.
	www.ll.mit.edu /asap/asap_95/abstract/16.html (205 words)

	Topology Research
		I'm kind of obsessed with topology efficiency, and here's my ongoing attempt to come up with the most efficient prototype topology that can be used for characters of any age, sex, or race.
		The darker lines are the basic topology, and the lighter lines are the more detailed splits.
		This one is Steven Stahlberg's level zero Sub'D base mesh in Maya.
	www.ethereality.info /ethereality_website/3d/topology_research/topology_research.htm (669 words)

	topology
		Two variations of the star topology used by most larger Ethernet networks today are the star bus and star tree topologies.
		Essentially, the star bus topology has multiple data closets interconnected by bus trunk lines of thin net, while the star tree topology links multiple data closets with twisted pair or fiber optic.
		In a ring topology, the network signal is passed through each network card of each device and passed on to the next device.
	fallsconnect.com /topology.htm (1059 words)

	The Lewis Acid/Base Interaction Matrix
		The highest occupied molecular orbital (HOMO) of a Lewis base "reacts with" or "complexes with" or "interacts with" the lowest unoccupied molecular orbital (LUMO) of a Lewis acid to give a Lewis acid base complex with a bonding molecular orbital.
		In the 1960s, Ralph Pearson suggested that Lewis acids and Lewis bases should be classified as hard, borderline or soft, with the observation that: "Hard [Lewis] acids prefer to complex with hard [Lewis] bases and soft [Lewis] acids with soft [Lewis] bases", the HSAB principle (go here and here for more information).
		Lewis acid and Lewis base types which are rich in congeneric arrays interact to give complex types which are rich in arrays.
	www.meta-synthesis.com /webbook/13_lab-matrix/LAB_matrix.html (1513 words)

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