
	Where results make sense

Topic: Topos

	Topos - Wikipedia, the free encyclopedia
		A topos exists in which the axiom of choice is invalid.
		Another important example of a topos (and historically the first) is the category of all sheaves of sets on a given topological space.
		The historical origin of topos theory is algebraic geometry.
	en.wikipedia.org /wiki/Topos (1182 words)

	Background and genesis of topos theory - Wikipedia, the free encyclopedia
		General problems of so-called 'descent' in algebraic geometry were considered, at the same period when the fundamental group was generalised to the algebraic geometry setting (as a pro-finite group).
		The theory rounded itself out, by establishing that a Grothendieck topos was a category of sheaves, where now the word sheaf had acquired an extended meaning with respect to the idea of Grothendieck topology.
		The topos concept arose in algebraic geometry, as a consequence of combining the concept of sheaf and closure under categorical operations.
	www.sciencedaily.com /encyclopedia/background_and_genesis_of_topos_theory (1566 words)

	Mathematical topos
		A topos (plural: topoi or toposes - this is a contentious topic) in mathematics is a type of category which allows the formulation of all of mathematics inside it.
		In more interesting topoi, the axiom of choice may no longer be valid, or the the law of the excluded middle (every proposition is either true or false) may break down.
		For instance, constructivists may be interested in the topos of all "constructible" sets and functions in some sense.
	www.ebroadcast.com.au /lookup/encyclopedia/to/Topos.html (399 words)

	Topos Theory
		Topos theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas.
		The original notion of topos, as a `generalized space' suitable for supporting the exotic cohomology theories required in algebraic geometry, sprang from the fertile brain of Alexandre Grothendieck in the early 1960s, and was developed in his `Seminaire de Geometrie Algebrique du Bois-Marie' particularly during the academic year 1963-64.
		It is not addressed to those who are trying to learn about topos theory for the first time, but rather to those who already have some acquaintance with the subject and who wish to deepen their understanding, or to learn about aspects of it which they have not previously encountered.
	www.wordtrade.com /science/mathematics/topostheory.htm (3716 words)

	Topos - THE INTERNATIONAL REVIEW OF LANDSCAPE ARCHITECTURE AND URBAN DESIGN
		Topos – The International Review of Landscape Architecture and Urban Design is reporting on trail-blazing projects and plans from all over the world.
		Topos collaborates closely with the International Federation of Landscape Architects and the International Society of City and Regional Planners, and maintains a tightly-knit network of correspondents to keep it abreast with the latest developments in landscape architecture and urban design.
		The editors of Journal of Landscape Architecture, JoLA continue to invite colleagues to adress and shape the agenda for the second issue of JoLA by submission of articles to all three sections of the journal before June 20th.
	www.topos.de (331 words)

	Topos - Wikipedia
		Der Topos in der Grammatik ist ein konkreter Ort als Stellung eines Wortes oder Satzes.
		In den Geistes- und Kulturwissenschaften wird der Begriff Topos sowohl für Kategorien, als auch für (Vorstellungs-)Bilder verwendet.
		Topos (Mathematik) ist ein Begriff der Kategorientheorie mit Anwendungen in Geometrie und Logik sowie in der Informatik, insbesondere im Bereich der Datenbanken.
	de.wikipedia.org /wiki/Topos (304 words)

	Main Page (Site not responding. Last check: 2007-10-07)
		TOPOS 3.2/4.0 is a program package for multipurpose geometrical and topological analysis of crystal structures.
		TOPOS 3.2/4.0 is an integrated interactive shell including database management system (DBMS), which allows one to edit, search and retrieve crystal structure information, and a number of applied programs integrated into DBMS.
		TOPOS 3.2/4.0 also includes the converter programs from the Cambridge Structural Database, the Inorganic Crystal Structure Database text formats, and CIF formate to the TOPOS database format.
	www.topos.ssu.samara.ru (174 words)

	The Topos of Historicity
		Thus, the real topos of historicity is not in the stories and not in the documents but it is in the tradition which preserved the documents.
		The leaders of that tradition chose the documents based upon their connection with the original group withwhom the deposit of Christ's teachings were fist entrusted, the Apostles.
		The Topos of Historicity"Topos" is just a fancy Greek term used in arts and hummanities circles for "place," or "location." I bring this up because I think what is most important is the understanding of and acceptance of the Tradition itself.
	www.geocities.com /metacrock2000/Jesus_pages/topos.htm (3229 words)

	Topos: Facts and details from Encyclopedia Topic (Site not responding. Last check: 2007-10-07)
		A topos exists in which the axiom of choice axiom of choice quick summary:
		Another important example of a topos (and historically the first) is the category of all sheaves sheaf quick summary:
		In mathematics, a grothendieck topology is a structure defined on an arbitrary category c which allows the definition of sheaves on c, and with that the...
	www.absoluteastronomy.com /encyclopedia/t/to/topos.htm (2134 words)

	[No title]
		Actually, I heard the word topos a rather >large number of times and still don't know what it is! This begins to >be annoying, if you know what I mean...
		After a bunch of work, Lawvere and others invented the concept of a "topos", which is category with certain extra properties that make it a lot like the category of sets.
		Then you might want to work in the topos of presheaves on X, or the topos of sheaves on X. Sheaves are important in twistor theory and other applications of algebraic geometry and topology to physics.
	www.math.niu.edu /~rusin/known-math/00_incoming/topos (912 words)

	Topos (Site not responding. Last check: 2007-10-07)
		In mathematics, a topos (plural: topoi or toposes - thisis a contentious topic) is a type of category which allows theformulation of all of mathematics inside it.
		Traditionally, mathematics is built on set theory, and all objects studiedin mathematics are ultimately sets and functions.It has been argued that category theory could provide a betterfoundation for mathematics.
		For instance, constructivists may be interested in the topos of all"constructible" sets and functions in some sense.
	www.therfcc.org /topos-138448.html (958 words)

	The Modified Realizability Topos (Site not responding. Last check: 2007-10-07)
		The modified realizability topos is the semantic (and higher order) counterpart of a variant of Kreisel's modified realizability (1957).
		In this paper this topos is investigated from a general logical and topos-theoretic point of view.
		It is shown that Mod (as we call the topos) is the closed complement of the effective topos inside another one; this turns out to have some logical consequences.
	www.brics.dk /RS/96/3 (115 words)

	Topos (Site not responding. Last check: 2007-10-07)
		It is also possible to encode a logical theory, such as the theory of all groupss, in a topos.
		Lawvere realized the logical content of this structure, and his axioms lead to the current notion.
		John Baez: Topos theory in a nutshell,." class="external">http://math.ucr.edu/home/baez/topos.html.
	bopedia.com /en/wikipedia/t/to/topos.html (597 words)

	An introduction to fibrations, topos theory, the effective topos and modest sets
		Abstract: A topos is a categorical model of constructive set theory.
		In particular, the effective topos is the categorical `universe' of recursive mathematics.
		Chapter 3 is an exposition of some basic topos theory, and explains why a topos can be regarded as a model of set theory.
	www.lfcs.informatics.ed.ac.uk /reports/92/ECS-LFCS-92-208 (301 words)

	Is 'topos' a meaningful term?
		"Topos: from a Greek word meaning 'place', a 'topos' in poetry is a 'commonplace', a standard way of describing a particular subject.
		"The word topos is used in rhetoric to denote a commonplace-the proper subject of dialectical and rhetorical syllogisms-which may deal with such questions as justice or politics and may be of various, identifiable types.
		The topos form contains the following elements: (1) an injunction urging that a certain course of behavior be followed or avoided, (2) a reason for the injunction, and (3) a discussion of the logical or practical consequences of the behavior.
	www.robotwisdom.com /issues/topos.html (755 words)

	TOPOS AND ENTHYMEME [
		Most agree that two of the crucial terms of the Rhetoric are topos and enthymeme, that the relation between them is important, and that the explication of neither is clear.
		By an element [of an enthymeme] I mean the same thing as a commonplace [topos]; for an element is a commonplace embracing a large number of enthymemes.
		In other words, the definitions of topos (3.1) and enthymeme (4.1) are adequate to the treatment of the topos "the More and the Less" and the enthymemes constructed using it.
	www.wtc.ab.ca /tedyck/top.enth.00.htm (3204 words)

	topos
		Okay, you wanna know what a topos is? First I'll give you a hand-wavy vague explanation, then an actual definition, then a few consequences of this definition, and then some examples.
		Or, you might like to work in the topos of sheaves on a topological space - or even on a "site", which is a category equipped with something like a topology.
		This is a great introduction to category theory via the topos of sets: it describes ordinary set theory in topos-theoretic terms, making it clear which axioms will be dropped when we go to more general topoi, and why.
	math.ucr.edu /home/baez/topos.html (1839 words)

	[No title] (Site not responding. Last check: 2007-10-07)
		He defined it as a category IB with pullbacks such that each slice is an elementary topos and the reindexing functors f* are logical and have right adjoints Pi_f.
		Nevertheless this definition of partial topos as a category all whose slices are toposes has a certain defect - pointed out by Benabou himself - namely that ANY groupoid is a partial topos as it has pullbacks and any slice is the trivial topos.
		LEMMA 4 IB is a partial topos iff (i) IB has pullbacks and binary products (ii) any f* has a right adjoint Pi_f (iii) for any I the category IB/I has a subobject classifier (i.e.
	www.mta.ca /~cat-dist/catlist/1999/partial-topos (579 words)

	Digital Elevation Modeling and Mapping Digital Elevation Model
		Creation of a DEM from a topographic map requires that the elevation contours on the topo map be somehow converted to xyz data.
		Sometimes a raster topo of sufficiently high resolution will already be available in TIF or other graphic file format.
		In general, if your raster source is not at least as good as a USGS topo downloaded from an archive like gisdatadepot.com you will be much better off scanning a paper map to create the necessary input image.
	www.terrainmap.com /rm19.html (2123 words)

	Giving Teeth to Topos, based on Mike Holmes' comments
		Topos is described in the thread "Ed Designs a Game: Topos" and a copy of the rules is available at http://www.remove-this-part-lostthoughts.org/phpwiki/index.html/Topos.
		I like Topos the way it is, but Mike's challenges have made me curious whether there could be a version of Topos that has more "teeth" that still fulfills my design goals.
		Another thought, that would change Topos perhaps more than you would like, is to allow each player to have one single non-changeable Group Topos each.
	www.indie-rpgs.com /forum/index.php?t=6892&highlight=topos (2024 words)

	Citations: Some remarks on free monoids in a topos - B'enabou (ResearchIndex) (Site not responding. Last check: 2007-10-07)
		An algebra for the corresponding 2 monad M = Cat(Cat Cat is a strict monoidal category, an algebra morphism is a strict monoidal functor and a 2 cell a monoidal natural transformation.
		This amounts to a C collection of functors x : f : y x F (y) F (x) It is clear 51 that such x s satisfying the algebra axioms, give the action on morphisms to endow F with the structure of a functor F : C Cat,....
		This amounts to a C collection of functors x : f : y x F (y) F (x) It is clear 57 that such x s satisfying the algebra axioms, give the action on morphisms to endow F with the structure of a functor F : C....
	citeseer.ist.psu.edu /context/1014453/0 (788 words)

	FISH Products: Our Favorite Topos, Yosemite and beyond.
		The way we have set it up is so at the top of the page, you have some notes by the ascent party, followed by the actual topo of the route.
		The topo itself may or may not have additional pitch by pitch notes.
		But, remember, these topos were updated by somebody who might have been drinking, mourning a lost loved one, or just full of it in general.
	www.fishproducts.com /topos/FavTopos.html (684 words)

	Geometry.Net - Pure And Applied Math Books: Topos Theory
		The book is long because it gives very explicit descriptions of many advanced topics--you can learn a great deal from this book that, before it was published, you could only learn by knowing researchers in the field.
		Sketches of an Elephant: A Topos Theory Compendiumm vol.
		Johnstone has a three-volume set on the current state of topos theory due to appear later this year.
	www.geometry.net /pure_and_applied_math_bk/topos_theory.html (729 words)

	Climbing Talk - Sweet!!! Topos for your HandHeld
		The Mallorca and El Chorro topos are almost identical to the topos in the 1996 Costa Blanca, Mallorca, El Chorro ROCKFAX.
		The Frankenjura topos are very similar to those published in a guidebook by German author Bernhard Thum.
		Although Coronn.com deny copying the topos they have offered no explanation as to why their diagrams contain all of the minor errors which were present in the 1996 ROCKFAX.
	www.climbingtalk.com /showthread.php?p=179 (204 words)

	United States, North America, Recreation, Climbing and By Region Page @ LocalColorArt.com (Local Color Art) (Site not responding. Last check: 2007-10-07)
		Arizona Bouldering - Photos, topos, route descriptions, and general area information for bouldering and climbing areas around Phoenix and Tucson.
		California Bouldering.com - Topos, photos, and information for the Sherwin Plateau, the Bachar Boulders, Clark Canyon, and the Geophysics Boulders.
		Topos for sale by download or in book format for Yosemite free climbs and big walls.
	recreation.texastrader.com /Recreation/Climbing/By_Region/North_America/United_States (1654 words)

Try your search on: Qwika (all wikis)