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Topic: Box topology

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Product topology

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	Encyclopedia :: encyclopedia : Topology (Site not responding. Last check: 2007-11-06)
		Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants.
		Topology has sometimes been called rubber-sheet geometry, because it does not distinguish between a circle and a square (a circle made out of a rubber band can be stretched into a square) but does distinguish between a circle and a figure eight (you cannot stretch a figure eight into a circle without tearing).
		In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures defined on arbitrary categories which allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories.
	www.hallencyclopedia.com /topic/Topology.html (1776 words)

	Intersecting Sequences of Iso-oriented Boxes
		The box intersection algorithm comes in two flavors: One algorithm works on a single sequence of boxes and computes all pairwise intersections, which is called the complete case, and used, for example, in the self-intersection test.
		The box intersection algorithm is implemented as a family of generic functions; the functions for the complete case accept one iterator range, and the functions for the bipartite case accept two iterator ranges.
		For the closed box topology, the center box in query intersects all boxes, and the upper-right box in query intersects the four boxes of the upper-right quadrant in boxes.
	www.ics.uci.edu /~dock/manuals/cgal_manual/Box_intersection_d/Chapter_main.html (2842 words)

	Box topology - Wikipedia, the free encyclopedia
		In general, the box topology is finer than the product topology, although the two agree in the case of finite direct products (or when all but finitely many of the factors are trivial).
		It is easily verified that B is actually a basis for the topology.
		This does not always hold in the box topology, because it is in general a much finer topology, so therefore mapping into the range space makes it much harder for functions to be continuous.
	en.wikipedia.org /wiki/Box_topology (656 words)

	PlanetMath: product topology
		The product topology is generally more useful than the box topology.
		The main reason for this can be expressed in terms of category theory: the product topology is the topology of the direct categorical product in the category Top (see Theorem 1 below).
		This is version 30 of product topology, born on 2002-06-12, modified 2006-10-01.
	planetmath.org /encyclopedia/ProductTopology.html (181 words)

	Managing the Passport 8000 Series Switch Using Device Manager Release 5.x.x
		The slot number in the chassis in which the topology message was received.
		The port on which the topology message was received.
		Indicates if the sender of the topology message is on the same Ethernet segment as the reporting agent.
	www25.nortelnetworks.com /library/tpubs/html/passport/313195A/05_Diags19.html (196 words)

	Point to Area Topology dialog box
		Areas — Retains (as a new topology layer) all areas that satisfy the interaction criteria of the two highlighted topology layers.
		Both — Retains (as a new topology layer) all points and areas that satisfy the interaction criteria of the two highlighted topology layers.
		The topology generated is a mixed topology layer — a topology layer that can contain points and areas.
	docs.bentley.com /en/PowerMap/geooutlkhelp1509.html (418 words)

	Amazon.com: Topology (2nd Edition): Books: James Munkres (Site not responding. Last check: 2007-11-06)
		I must say I was quite confused when I began the actual topology portion of the book (chapter 2), but this was due to the difficulty of topology, in general, and not the book itself.
		Unfortunately, this lack of a completely cohesive approach is unavoidable, since a course in point-set topology ought to provide a stepping stone one can use for further study in topology and not a mountain one can climb and conquer and thus know the subject completely.
		If you are searching for an introduction to point-set topology that will give you a solid grounding in the basics of point-set topology, but at the same time will give it to you in an easily approached manner, than this book is for you.
	www.amazon.com /Topology-2nd-James-Munkres/dp/0131816292 (1695 words)

	Intersecting Sequences of dD Iso-oriented Boxes
		Boxes can be interpreted by the box intersection algorithm as closed or as half-open boxes, see also Section 37.2.
		We create the same boxes as in the minimal example in Section 37.4.
		The example in the previous Section 37.7 uses an array to provide the coordinates and then creates another array for the boxes.
	www.cgal.org /Manual/3.2/doc_html/cgal_manual/Box_intersection_d/Chapter_main.html (2886 words)

	The Box Product Problem (Site not responding. Last check: 2007-11-06)
		Give it the box product topology instead (so open sets are unions of productts of open intervals).
		The topology of the line is generated by open intervals; i.e., (unions of) sets of form (a,b).
		The box topolgy is defined on all infinite products similarly, and a box product is the product, as sets, of topological spaces given the box topology.
	www.math.buffalo.edu /~sww/0papers/Box.Product.Problem.html (161 words)

	Line to Area Topology dialog box
		Lines — Retains (as a new topology layer) all lines that satisfy the interaction criteria of the two highlighted topology layers.
		Both — Retains (as a new topology layer) all lines and areas that satisfy the interaction criteria of the two highlighted topology layers.
		The topology generated is a mixed topology layer — a topology layer that can contain lines and areas.
	docs.bentley.com /en/PowerMap/geooutlkhelp1510.html (592 words)

	PlanetMath: box topology
		is a finite set, the box topology coincides with the product topology.
		(which is the same as the product topology) consists of all sets of the form
		Cross-references: index set, product topology, base, open sets, products, generalized Cartesian product, topological spaces
	planetmath.org /encyclopedia/BoxProduct.html (108 words)

	Box topology - Boxtopology
		Now consider the topology generated by the collection B = { Π Ui
		We call this the box topology (so called because in the case of R, the basis sets look like boxes or unions thereof).
		This actually makes the box topology very useful for providing counterexamples - many qualities such compactness, connectedness, metrizability, etc., if possessed by the factor spaces, are not in general preserved in the product with this topology.
	www.kopete.org /Box-topology.html (558 words)

	General Topology - NoiseFactory Science Archives (http://noisefactory.co.uk)
		If we assign P the discrete topology, in which every subset is open, these will include all the inverse images of open sets in the various factor spaces.
		The standard topologies on N, Z, Q, and R are all (defined to be) their order topologies.
		The topology on C is not an order topology - in fact, there is no possible ordering of the complex field which generates the standard topology.
	noisefactory.co.uk /maths/topology.html (4788 words)

	SQL Server 6.0 Setting Up Replication (Site not responding. Last check: 2007-11-06)
		The server publication options determine the servers that are authorized to subscribe to this server’s publications, the schedule by which replication will be performed for each subscription server, which of this server’s databases are authorized to publish data, and the directory used as the distribution working directory.
		In the Replication – Distribution dialog box, select the servers that will be permitted to use this server as their remote distribution server.
		The Replication Topology window provides a convenient way to view the replication relationships of a server, to add subscription servers, and to open the replication management dialog boxes that are provided by SQL Enterprise Manager.
	www.ctlcorp.com /support/sql/repl2.html (11310 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Using the box topology the product of compact sets need not be compact).
		Another classical use of Tychonoff'Theorem in functional analysis is Banach-Alaoglu's Theorem: In the dual space of a Banach space, the unit ball is compact for its weak topology.
		This result often makes up for the fact that the unit ball is not compact for its metric topology, when the space is infinite-dimensional.
	www.math.niu.edu /~rusin/known-math/95/tychonoff (488 words)

	Specifying Chained Requests
		TOPOLOGY is the PDP Module to which the request is mapped.
		PDP Action Value (for Set requests): From the combo box select an action type, to be performed on the PDP Parameter name (PDP Action), when the request is called.
		Is Filter: To set a PDP name as a filter, select the check box.
	www.kenati.com /downloads/WebHelp/understanding_npblox_cli_ide/chained_requests/specifying_chained_requests.htm (845 words)

	Managing the Passport 8000 Series Switch Using Device Manager Release 5.x.x
		Table 71 describes the Topology tab fields on the Diagnostics dialog box.
		The value of sysUpTime the last time an entry in the network management MIB (NMM) topology table was added, deleted, or modified.
		The maximum number of entries in the NMM topology table.
	www25.nortelnetworks.com /library/tpubs/html/passport/313195A/05_Diags18.html (135 words)

	Cisco MDS 9000 Family Fabric Manager Configuration Guide, Release 2.x - Inter-VSAN Routing Configuration [Cisco ... (Site not responding. Last check: 2007-11-06)
		User configured topology entries that are not part of the network are aged out in about three minutes.
		IVR topology in auto mode requires Cisco MDS SAN-OS Release 2.1(1a) or later and enabling CFS for IVR on all switches in the fabric.
		The VSAN topology configuration must be updated before a border switch is added or removed.
	www.cisco.com /en/US/products/ps5989/products_configuration_guide_chapter09186a008040fa3a.html (5540 words)

	FPGA Architecture for the Challenge
		By turning on some of the programmable switches within a switch box, longer paths can be constructed.
		In this architecture, when a wire enters a switch box, there are three programmable switches that allow it to connect to three other wires in adjacent channel segments.
		In this switch box topology, a wire in track number one connects only to wires in track number one in adjacent channel segments, wires in track number 2 connect only to other wires in track number 2 and so on.
	www.eecg.toronto.edu /~vaughn/challenge/fpga_arch.html (804 words)

	Hagerman Technology LLC: Reviews
		The no-frills design emphasizes components of exceptional quality, implementing an expensive balanced circuit topology (double the number of tubes) and choke regulated supplies.
		Since there were good specifications for the triode-connected 6L6 in the tub manual, I ran sample #1 in triode mode.
		Next up were the IEC Mullard EL34s, which came in a singl box marked "lab-matched balanced pair." According to the scope traces (Figs.
	www.hagtech.com /reviews.html (7015 words)

	Equivalence of the Box/Ball topology - Vectorcalcumb
		So, when we say that the ball and box topology are equivalent, we mean that for any neighbhorhood in either, there is a neighbhorhood in the other which contains the original neighbhorhood, right?
		On going to write just now, I had thought that this was clearly impossible, since you can't square the circle, but apparently you can square the circle, just not with a ruler and compass(Which, of course makes perfect sense, it's just a square with
		However, it still seems to me that even if we have a neighbhoorhood of equal area(volume, extent) around a point, we can't possibly have an elementwise identical neighbhoorhood in the other topology, just one defined to have the same extent in the other topology.
	editthis.info /VectorCalcUMB/Equivalence_of_the_Box/Ball_topology (164 words)

	Field-programmable gate array (Site not responding. Last check: 2007-11-06)
		Unsegmented FPGA Routing Whenever a vertical and a horizontal channel intersect There is a switch box.
		The pattern, or topology, of switches used in this Architecture is the planar or domain-based switch box topology.
		To define the behaviour of the FPGA it is required to use a Hardware Description Language (HDL) or a schematic designed using an Electronic Design automation tool.
	field-programmable-gate-array.iqnaut.net (999 words)

	Inter-VSAN Routing Configuration
		When auto IVR topology is turned on it starts with the previously active, if any, manual IVR topology.
		Auto topology then commences its discovery process, and may come up with new, alternate or better paths.
		In user-configured VSAN topology mode, the AFIDs are specified in the VSAN topology configuration itself and a separate AFID configuration is not needed.
	www.cisco.com /univercd/cc/td/doc/product/sn5000/mds9000/3_0/fmcfg/part4/ivr.htm (7103 words)

	Transcend Enterprise Manager for UNIX v4.2.1 Device View User Guide
		An example of the dialog box is shown in Figure 7-4.
		An example of the dialog box is shown in Figure 7-5.
		An example of the dialog box is shown in Figure 7-6.
	support.3com.com /infodeli/tools/netmgt/temunix/temu42/1039dv/chap72.htm (451 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		>> box topology on the Hilbert cube is finer that this.
		The assertion is that it induces the same topology on
		>> The box topology on R^N is that for which the collection of all infinite
	mathforum.org /kb/plaintext.jspa?messageID=3713199 (182 words)

	Index (Site not responding. Last check: 2007-11-06)
		Maximum number of distributed processes (entry box in front end)
		Number of Islands (entry box in front end)
		Number of Operations (entry box in front end)
	www.ccdc.cam.ac.uk /support/documentation/gold/3_0/doc/portable_html/IX.html (572 words)

	3. functional separation
		In 1923 Tietze first gave the definition of a topology, called the box topology, on a product of infinitely many spaces to be that which is generated by the product of open sets
		Clearly, Tietze's topology is not good for proving theorems in infinite products (e.g., the preservation of compactness, connectedness, metric etc.), and thus we use a product topology
		which, like compactness, extends finite delicately - the topology is generated by a product of open sets which, only finitely often, may be different from the entire factor:
	www.math.buffalo.edu /~sww/classes/COMPACT/COMPACT3.html (423 words)

	SCOTT W. WILLIAMS'VITA
		For the mathematics field of Topology in general, browse Topology Atlas.
		Orderable subspaces of Cech-Stone remainders, Topology Proceedings 7 (1982), 301-327.
		Modern General Topology with Dynamics and Homotopy (working title), previously known as The Black Arts of Topology with Homotopy - an undergraduate/graduate textbook (Ms.
	www.acsu.buffalo.edu /~sww/mathbio.html (1334 words)

	hagerman
		Usually it is of the current feedback variety, used to tame an extremely nonlinear pentode output stage.
		Most designers don't even realize it is a current feedback topology (back to the cathode of input tube).
		(Balanced outputs are available as an option, though the test unit did not have them.) The outboard transformer box is necessary even with medium output moving coils like my Benz Ruby 2H at.8mv, so all listening was done that way.
	www.positive-feedback.com /Issue11/hagerman.htm (4197 words)

	Dror Bar-Natan: Classes: 2004-05: Math 1300Y - Topology
		Class notes for Thursday September 30, 2004 (non-metrizability of products in the box topology, non-metrizability of uncountable products, sequences and sequencial closure, clopens and connectedness)
		Class notes for Tuesday October 5, 2004 (connected sets, intervals are connected, finite and infinite products are connected, connectedness in the box topology, connectedness and path-connectedness)
		Class notes for Thursday March 3, 2005 (the topology of Δ-complexes, degrees and their basic properties)
	www.math.toronto.edu /~drorbn/classes/0405/Topology/index.html (1104 words)

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