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Topic: Pointless topologies

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	Topology - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-05)
		Topology (Greek topos = place and logos = word) is a branch of mathematics concerned with the study of topological spaces.
		Topology is concerned with the study of the so-called topological properties of figures, that is to say properties that do not change under bicontinuous one-to-one transformations (called homeomorphisms).
		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.
	encyclopedia.worldsearch.com /topology.htm (1315 words)

	Topology - LearnThis.Info Enclyclopedia (Site not responding. Last check: 2007-11-05)
		In mathematics, topology is a branch concerned with the study of topological spaces.
		Topology is also concerned with the study of the so-called topological properties of figures, that is to say properties that do not change under bicontinuous one-to-one transformations (called homeomorphisms).
		The root of topology was in the study of geometry in ancient cultures.
	encyclopedia.learnthis.info /t/to/topology_1.html (1288 words)

	Pointless topology (Site not responding. Last check: 2007-11-05)
		Pointless topology (also called point-free or pointfree topology) is an approach to topology which avoids the mentioning of points.
		Pointless topology then studies lattices like these abstractly, without reference to any underlying set of points.
		While many important theorems in point-set topology require the axiom of choice, this is not true for their analogues in locale theory.
	www.worldhistory.com /wiki/P/Pointless-topology.htm (457 words)

	Watches-Sheaves in Geometry and Logic - A First Introduction to Topos Theory -Universitext- (Site not responding. Last check: 2007-11-05)
		From the standpoint of ordinary topology, the Heyting algebra is significant in that the algebra of open sets is not Boolean, i.e.
		A Grothendieck topology on a category is thus a function that assigns to each object in the category a collection of sieves on the object (this function must have certain properties which are discussed by the authors).
		When considering the notion of the Grothendieck topology, the authors define the notion of a `site', which is essentially a (small) category along with a Grothendieck topology on the category.
	www.minihttpserver.net /z_watches/A_sheaves_in_geometry_-0387977104.htm (1631 words)

	Comparison Tool (Site not responding. Last check: 2007-11-05)
		In topology and related areas of mathematics comparison of topologies refers to the fact that two topological structures on a given set may stand in relation to each other.
		See topologies on the set of operators on a Hilbert space for some intricate relationships.
		All possible polar topologies on a dual pair are finer than the weak topology and coarser than the strong topology.
	www.wwwtln.com /finance/44/comparison-tool.html (961 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		They also discovered that the process of turning a ``presheaf'' into a sheaf was implicitly involved in the notion of forcing used by Cohen in his proof of the independence of the Continuum Hypothesis -- and by Scott and Solovay in the corresponding ``Boolean valued'' models of set theory.
		Since topologies can be described in terms of open sets, with little mention of points, it is possible to discuss ``pointless'' spaces, or locales, and the corresponding topoi of sheaves (Section).
		The next section discusses representations of topoi in terms of such pointless spaces, including the theorem of Freyd showing how every topos can be embedded, in a suitably nice way, in the category of equivariant sheaves on some locale.
	www.elsevier.com /homepage/saj/523281/h14.htm (667 words)

	REVIEW: "Building Secure Wireless Networks with 802.11", Jahanzeb Khan/Anis Khwaja (Site not responding. Last check: 2007-11-05)
		The discussion does not build on that from chapter one to, for example, point out that ad hoc wireless networks are similar to bus topologies, while infrastructure networks are more akin to stars.
		However, there is a great deal of material repeated from prior text (the discussion of spectrum is reprised almost word for word), and, other than some frequency and maximum bandwidth information, there is little additional detail.
		Most of it is irrelevant to the specific needs of wireless situations or is not discussed in terms of the particular needs of wireless networks.
	talkaboutabook.com /group/misc.books.technical/messages/19248.html (917 words)

	Citebase - POINTLESS SPACES IN GENERAL RELATIVITY
		As an example, a toy model producing spacetimes of four points with different topologies is presented.
		The latter is described in terms of histories approach to quantum theory.
		and Technol., Vienna, June 3 - 6, 1995 The machinery is suggested to describe the varying spacetime topology on the level of its substitutes by finite topological spaces.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:gr-qc/9503048 (895 words)

	threads or queue for this task (Site not responding. Last check: 2007-11-05)
		It goes without saying that if the designer knows in advance that he doesn't have the throughput to handle incoming requests, then a significantly more complicated solution is called for.
		I alluded to more complex topologies and scenarios but I lacked the time and patience to spell out the solutions.
		Attempting to do so seemed doubly pointless as you seemed to be taking the lead on more elaborate scenarios.
	mail.python.org /pipermail/python-list/2002-September/123018.html (1707 words)

	Speed Comparison Perl Python & C (Site not responding. Last check: 2007-11-05)
		I've just spent a day finding and fixing an algorithm which turned out to be O(n^3) in some legacy code (in-memory representation of an XML file for network topologies).
		It was fine for the small, initial topologies that it was developed for.
		Unfortunately, it didn't scale overly well to the somewhat larger topologies I'm dealing with now...
	mail.python.org /pipermail/python-list/2004-March/209993.html (252 words)

	Firewall RISKS
		If you don't have a handle on these issues, the rest will be pretty much pointless.
		That all aside, and also ignoring that home dialup use is probably one of the functions with the -least- specialised topology, I would still point out that (from this end at least) observing that a security setup is `specialized' is in no way a Bad Thing.
		We seem to have made some progress, though, as you originally appeared to be tacitly suggesting (if not outright asserting) that a firewall was necessary for -any- topology.
	list.nfr.com /pipermail/firewall-wizards/1999-June/005632.html (1038 words)

	lattic semiconductor
		in other words, can a topology t, be given m so that (m,t) homeomorphic (s,tau) ?
		thus can i not describe a t1 topology entirely by the topology tau without reference to the points?
		is there something i'm not seeing what places sobriety in a paramount place for t1 spaces regards pointless topologies?
	www.ins-inc.net /lattic/semiconductor (1287 words)

	Wireless Security End to End, Brian Carter/Russell Shumway, 2002
		Network intrusion protection is said, in chapter five, to consist of firewalls and other tools with limited application to wireless topologies.
		In regard to network intrusion detection, some of the material in chapter six is pointless (who would expect an intrusion detection system (IDS) to protect against insider attacks?) and some is wrong (a honeypot would only act as an intrusion detection sensor by chance).
		Chapter seven has sound information on host-based IDS and some advice on hardening systems, but wireless networking is almost unmentioned.
	www.iwar.org.uk /reviews/netsec/wireless-security-end-to-end.htm (464 words)

	Inequality. Many-to-Many: (Site not responding. Last check: 2007-11-05)
		I've spent a good part of the last 3 years looking at various network topologies, both social and technological, and have yet to run into a large, heterogenous and robust system that doesn't resolve into powerlaw distributions of link density.
		Enabling the pursuit of happiness is one thing but changing the topology to somehow enforce happiness seems wrongheaded to me.
		Nobody owns the substrate of the blogosphere and nobody will ever be able to mandate any artificial cost scheme over enough connections to make a difference to topology of the network as a whole.
	www.corante.com /many/archives/2004/01/13/inequality.php (4832 words)

	OpenP2P.com: Peer and Web Services are Technologies of Connection and Coordination
		The point that email is a P2P application, both socially and architecturally, was made elegantly by Nelson Minar, former CTO of Popular Power.
		He evaluated client/server, ring, hierarchical, and mesh topologies along key measures including extensibility, information coherence, and fault tolerance.
		To be 100% pure P2P is as pointless as to be 100% pure Java or Perl or Windows or Linux.
	www.openp2p.com /pub/a/p2p/2001/11/09/udell.html (1076 words)

	Discussion@SR > Serial ATA? Seems kinda pointless to me.... (Site not responding. Last check: 2007-11-05)
		And since serial ATA drives will obviously be 7200rpm that bandwidth headroom seems as pointless as the 133mb/s head room that ata133 has.....
		Remember, USB and twisted pair ethernet require star topologies, but you may have noticed that they support more than a single device.
		May 7 2002, 10:51 AM For joe-average perhaps it is pointless...
	forums.storagereview.net /lofiversion/index.php?t3081.html (2350 words)

	[No title] (Site not responding. Last check: 2007-11-05)
		Similarly, all of the predictions of GR still hold in the regime in which the metric can be consstently expanded as a flat space metric plus a (not necessarily small) perturbation.
		The first definition I remember is that a W-algebra is a -subalgebra of the bounded linear operators on a Hilbert space that is closed in the weak topology.
		I think there's a theorem that every compact convex set in a topological vector space is the convex hull of its extreme points (which in the present example are the pure states).
	math.ucr.edu /home/baez/PUB/debate2000 (17309 words)

	AMCA: Some Results on Simple Quantales by Jan Paseka
		This work is intended as a step towards the development of the non-commutative topology using the approach of the theory of (involutive) quantales developed by C.J. Mulvey, J.W. Pelletier and J. Rosický.
		Quantales are certain partially ordered algebraic structures which generalize frames (pointless topologies) as well as various lattices of multiplicative ideals from ring theory and functional analysis (C
		The relations on a set, under the operation of relational composition, also form an involutive quantale.
	at.yorku.ca /c/a/a/i/84.htm (306 words)

	[No title]
		If E is a pre-ordered set, then a subset X of E is _cofinal_ with (to?) E if each element of E is dominated by some element in X. Example: a base for a topology is cofinal for the open sets.) _Coinitial_ is the dual condition.
		A preordered set E is _filtered_ (filtrant) on the left if every non-empty finite subset of E is bounded above by an element of E. Similarly for filtered on the right.
		a basis of the topology, not "base" as in "base change") to a sheaf: 1.
	math.stanford.edu /~vakil/ega0 (5238 words)

	NOEMA > IDEAS
		It should be clear that I regard any definition of hackers (...) as quite pointless: it is the purpose of this article to describe the semiotic fight of the term, not to state a scholarly definition.
		Without the help from influential hacker figures, this endeavor, of course, would have been impossible.
		So let me present a few examples of work, new examples that I hope can be seen as visual topologies, that though visual, I can imagine as being scores for computational music or sound.
	www.noemalab.org /sections/ideas/ideas_22.html (631 words)

	Alachisoft releases NCache 1.0 for .NET (Site not responding. Last check: 2007-11-05)
		Performance monitoring is also built into this tool, so customers immediately see how their application is performing and how each server in the server-farm is contributing toward this performance.
		NCache also provides a wide range of clustering topologies, including Replicated Cache, Partitioned Cache, and Near Cache topologies.
		Replicated Cache is intended for the most read-intensive applications and keeps copy of the entire cache on each node on the cluster.
	programmersheaven.com /app/news/DisplayNews.aspx?NewsID=4103&ZoneID=0 (419 words)

	Toposes Pour Les Vraiment Nuls - Vickers (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		...a practical level, constructive reasoning can thus can lighten the burden of topological discussion; at a deeper level it is hoped that the approach can bring a true reconcilliation between topology and effective mathematics.
		Further exposition of these ideas can be found in [8] and...
		Expositionally, though we are working with locales, we experiment with a new approach to them as topology free spaces, as outlined in
	citeseer.ist.psu.edu /481412.html (395 words)

	Firewall RISKS (Site not responding. Last check: 2007-11-05)
		In >fact, stop reading now and figure out answers to the above before >going on.
		I've got a fine handle on those issues.
		Setups involving >dialup to ISPs constitute less that one percent of all topologies?
	honor.icsalabs.com /pipermail/firewall-wizards/1999-June/005770.html (728 words)

	The Good News and the Bad News Department
		This initiative entails a basic change of the network topologies from "spoke and hub" to an infinite peer-to-peer "connectionless" mesh free of Ethernet and TCP/IP.
		The best way to envision this is to imagine the national air transport system changing from a spoke-and-hub arrangement with air traffic controllers to a wide-open free-for-all where you go where you want, when you want.
		It's a topology similar to what we have in the office with routers and hubs.
	www.pcmag.com /article2/0,1895,1601505,00.asp (950 words)

	Dr. Ahmed Ibrahim El-Maghrabi (Site not responding. Last check: 2007-11-05)
		in 1995 under title On Pointless Topologies from Faculty of Science, Tanta University, Tanta, Egypt.
		Ph.D. in 2000 under title A Study of Topological Concepts via Frames from Faculty of Science, Tanta University, Tanta, Egypt.
		General Topology, Frames, Generalized of closed sets, Rough sets.
	math.vanderbilt.edu /~schectex/temp/topol/50.htm (341 words)

	Version 1.6 of Vector Graphics ActiveX component is released (Site not responding. Last check: 2007-11-05)
		Moreover, the developer can associate graphic shapes with data to simplify data storage, search and retrieval of additional information from databases.
		By connecting shapes, the developer can create various topologies and layouts for quick calculations.
		Vector Graphics ActiveX is designed for Windows 2000/XP/2003 Server and distributed as a freeware for non-commercial use.
	www.programmersheaven.com /d/click.aspx?ID=N3939&Rss=True (343 words)

	The Long Tail: What is the Long Tail?
		Mass markets and their triumph built a culture, a cultural gradient, a cultural topology, a culture of one that ignored the cultures of the many.
		When business people talk about busting silos, they are basing that notion on homogenous technologies that ignored the cultural topology.
		The right software won't bust silos, but will use the cultural topologies in multi-culture corporations without insisting on line supremacy, without disregarding the economic benefits of the division on labor.
	longtail.typepad.com /the_long_tail/2005/01/what_is_the_lon.html (12320 words)

	NZMS Newsletter No 77
		The debate on when the 3rd millennium starts and the 2nd ends is a bit pointless from most points of view - noting especially the similar comments made by our Editor a little while ago.
		Our first four Doctors of Philosophy in Topology graduated in September: Jiling Cao from China, Sina Greenwood from NZ (with Samoan ancestry), Abdul Mohamad from Iraq and Tsukasa Yashiro from Japan.
		(Heriot-Watt University in Edinburgh), “Loopy geometry and topology”.
	ifs.massey.ac.nz /mathnews/Nzms77/news77.htm (13388 words)

	Peeve Farm
		See {Blogger, BlogSpot, LiveJournal}.] A stream-of-consciousness Web journal, containing links, commentary, and pointless drivel.
		UPDATE: As clarified by Kris, the big AppleTalk settling-out test actually occurred in 1989, when the new Ethernet-based implementation of AppleTalk (called EtherTalk) was being developed.
		Prior to that, AppleTalk was designed to operate over serial cables, and because of the characteristics and limitations of serial topologies, the settling-out behavior wouldn't have been anywhere near as dramatic as it was over Ethernet.
	www.grotto11.com /blog/archive/1028148491.shtml (1529 words)

	diyAudio Forums - Class A with AB Output-stage
		Still, it is possible to get an almost perfect transition from class A to class AB if you do it right.
		I'm quite happy to argue the various merits of AB topologies
		but given the original question I think its fairly pointless here.
	www.diyaudio.com /forums/showthread.php?postid=273047 (803 words)

	GameDev.net - Book Details - AI Techniques for Game Programming (Site not responding. Last check: 2007-11-05)
		You will learn about backpropagation and pattern recognition and discover how to train a network to recognize mouse gestures.
		Finally, the book explains state-of-the-art techniques for creating neural networks with dynamic topologies.
		No wasting time trying to solve pointless math equations here!
	www.gamedev.net /columns/books/bookdetails.asp?productid=199 (638 words)

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