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	Gluing axiom - Wikipedia, the free encyclopedia
		In mathematics, the gluing axiom is introduced to define what a sheaf F on a topological space X must satisfy, given that it is a presheaf, which is by definition a contravariant functor
		This is a logical matter: axioms for a local ring require use of existential quantification, in the form that for any r in the ring, one of r and 1 − r is invertible.
		The gluing axiom of sheaf theory is rather general.
	en.wikipedia.org /wiki/Gluing_axiom (1273 words)

	Sheaf - Biocrawler (Site not responding. Last check: 2007-10-20)
		The second step is to introduce an additional axiom, called the gluing axiom or the sheaf axiom, which captures the idea of gluing local information to get global information.
		Suppose X is a topological space, and C is a category (often, this is the category of sets, the category of Abelian groups, the category of commutative rings, or the category of modules over a fixed ring).
		Here the gluing axiom will be given in a form that requires C to be a concrete category.
	www.biocrawler.com /encyclopedia/Sheaf (2980 words)

	Gluing Axiom \| Gluing Porous Plastic (Site not responding. Last check: 2007-10-20)
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	drbi.info /gluing-axiom.htm (519 words)

	[No title]
		Definition 1.1 A model category M satisfies the cube axiom if for every commuta* tive cubical diagram in M in which the bottom face is a homotopy push-out square and * all vertical faces are homotopy pull-back squares, then the top face is a homotopy * *push-out square as well.
		The cube axiom now states that the top face is a homo* *topy push-out and we are done.
		With the restricted join axiom we would have to impose the addi* *tional restriction on B that B be S-cellular.
	www.math.purdue.edu /research/atopology/Chataur-Scherer/fibrewise.txt (3870 words)

	[No title]
		The axioms are: CF1: All isomorphisms of M are weak equivalences, and all isomorphisms with the domain a cofibrant object are trivial cofibrations.
		The axioms are: F1: All isomorphisms of M are weak equivalences, and all isomorphisms with fibrant codomain are trivial fibrations.
		M4: (Lifting axiom) Cofibrations have the LLP with respect to trivial fib* *ra- tions, and trivial cofibrations have the LLP with respect to fibrations.
	hopf.math.purdue.edu /RadulescuBanu/cofib-cat.txt (15946 words)

	Gluing Axiom \| 2002isuzuaxiom (Site not responding. Last check: 2007-10-20)
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	www.cyclingnews.com news and analysis
		Jones' primary axiom is: "The safety of the rider is paramount." The methodology that he recommends in his CyclingNews article is founded upon this axiom.
		Because the Tufo gluing tape works better than glue, is easier to change a flat (achieving a permanent repair), and takes ten minutes to put a pair of tires on when you get good.
		I agree that some of the latest instructions for gluing tubs seem like they were written by liability laywers, however Fastack is well known to dissolve the glue holding the tires base tape to the casing, especially with Continental tires.
	www.cyclingnews.com /tech.php?id=tech/2003/letters/june19b (2916 words)

	Single Driver Website
		I started gluing up the cabinet pieces beginning with the speaker frame and the top of the cabinet being glued to the side first.
		Since there are not really clamps to hold these pieces in place, lay the cabinet side on the floor or a sturdy table, glue both pieces and fit together.
		When gluing the pieces to the sides, start with the speaker frame and working your way through the horn in succession.
	melhuish.org /audio/DIYRH3.html (1377 words)

	sci.math FAQ: Cutting a Sphere
		If the pieces are polygons [or any piece with a nice boundary] you can permit them to be glued along their boundaries, ie the interiors of the pieces disjoint, and their union is the desired figure.
		* Using the axiom of choice on non-countable sets, you can prove that a solid sphere can be dissected into a finite number of pieces that can be reassembled to two solid spheres, each of same volume of the original.
		There is a finite collection of disjoint open sets in the unit cube in R^3 which can be moved by isometries to a finite collection of disjoint open sets whose union is dense in the cube of size 2 in R^3.
	www.cs.uu.nl /wais/html/na-dir/sci-math-faq/sphere.html (875 words)

	Grothendieck topology - ExampleProblems.com
		Then a presheaf on X is a contravariant functor from O(X) to the category of sets, and a sheaf is a presheaf which satisfies the gluing axiom.
		Lastly, the identity axiom corresponds to the idea that any set is covered by all its possible subsets.
		In fact, it is possible to put these axioms in another form where their geometric character is more apparent.
	www.exampleproblems.com /wiki/index.php/Grothendieck_topology (1308 words)

	Hunkler Gluing \| Gluing Axiom (Site not responding. Last check: 2007-10-20)
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	aodf.info /hunkler-gluing.htm (494 words)

	GoodSound! "Equipment" Archives
		In comparison, the Axiom EP175 is rated at 175W and 32-150Hz, the PSB 6i at 225W and 29-150Hz.
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		The differences between the Axiom and the Woodard were less noticeable at normal listening levels.
	www.goodsound.com /equipment/woodard_pro_12_sport.htm (1835 words)

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	eseh.info /gluing-axiom.htm (285 words)

	Sheaf (mathematics) - Wikipedia, the free encyclopedia
		The hypothesis of the gluing axiom is that the {f
		For simplicity, we will state the gluing axiom only when C is a concrete category.
		Sometimes the gluing axiom is split into two axioms, one for existence and one for uniqueness.
	en.wikipedia.org /wiki/Sheaf_(mathematics) (5337 words)

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	eseh.info /axiom-sandpiper-ii.htm (243 words)

	Tol-O-Matic, Inc. - Electric Linear Motion FAQs
		How can I decrease my gluing time cycle time and still follow my contoured pattern with a x-y axis?
		By using a third axis (SSC3) and a analog gluing gun, you can scale your glue flow rate by using the 3rd axis analog command output signal on the SSC.
		This way you can rapidly glue linear sections at a high rate of speed and slow down the x-y axis for the contour moves and set the glue feed rate at a lower flow rate into the corners.
	www.tolomatic.com /help/faqs.cfm?FAQ_CAT_ID=1 (990 words)

	Cutting a sphere into pieces of larger volume
		We are permitted to cut into finitely many polygons, to translate and rotate the pieces, and to glue along boundaries; then yes, any two equal-area polygons are equi-decomposable.
		Using the axiom of choice on non-countable sets, you can prove that a solid sphere can be dissected into a finite number of pieces that can be reassembled to two solid spheres, each of same volume of the original.
		This result is, nowadays, trivial, and is the standard example of a non-measurable set, taught in a beginning graduate class on measure theory.
	www.cs.uwaterloo.ca /~alopez-o/math-faq/node70.html (753 words)

	The Foundations of Mathematics and Mathematica (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-20)
		Well, I guess it was at the end of the 1800s, particularly following all the discoveries made by generalizing Euclid's axioms and so on, there got to be the idea that somehow mathematics could be thought of as a study of the consequences of appropriately chosen sets of axioms.
		But in the axiom setup in mathematics, one is usually interested in asking whether one can find any sequence of transformation rules that will get one from one particular expression to another.
		One can sort of pick here essentially the axioms for the multiway systems at random and one can ask, what then is the resulting behavior of the network of theorems associated with this multiway system.
	www.stephenwolfram.com.cob-web.org:8888 /publications/talks/IMS/imstalk.html (11949 words)

	GameDev.net - SciMath FAQ
		The axiom of choice is independent of the other axioms of set theory and can be assumed or not as one chooses.
		It is thus the platonic axiom par excellence, boldly asserting that a given set will always exist under certain circumstances in utter disregard of our ability to conceive or construct it.
		4) Using the axiom of choice on non-countable sets, you can prove that a solid sphere can be dissected into a finite number of pieces that can be reassembled to two solid spheres, each of same volume of the original.
	www.gamedev.net /reference/articles/article431.asp (3909 words)

	Trade my Polks for Axiom? - Page 2 - Audioholics Home Theater Forums
		With internet forums being axioms main way to get new customers you can imagine what happens when one customer who goes to 12 different forums saying how his axioms were bright and falling apart does to their reputation.
		On another note, The people here who are constantly reccomending axiom arent doing it because they are on the payroll, Although in some cases commison is paid for in-home auditions etc, which result in a purchase.
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	forums.audioholics.com /forums/showthread.php?p=212792 (2505 words)

	Antimeta (via CobWeb/3.1 planetlab2.tamu.edu) (Site not responding. Last check: 2007-10-20)
		Even in mathematics I'd like to say this is the case, both in arriving at standard axioms, in supporting new ones, and in developing conjectures.
		Say at some hypothetical future point in time, people have been led to adopt some axiom A of number theory that goes beyond PA (since PA is relatively weak, this might even be some consequence of ZFC, but it might not be).
		Because this axiom will be taken to be true of our concept of number, it will end up having an impact on various complicated computations in the natural sciences.
	www.antimeta.org.cob-web.org:8888 /blog (2775 words)

	Introduction
		To see that this is indeed the case imagine beginning with an octagon and gluing together the first and third, second and fourth, fifth and seventh, and the sixth and eighth sides.
		If we imagine gluing up our polygon into a surface embedded in three space, we can see what some of these conditions will be.
		In gluing up the octagon we also see that the sides that are glued together (identified with each other) must be of equal length.
	www.geom.uiuc.edu /apps/teich-nav/report/node1.html (1450 words)

	Question Corner -- Understanding Projective Geometry
		For instance, the basic axiom that "for any two points, there is a unique line that intersects both those points", when turned around, becomes "for any two lines, there is a unique point that intersects (i.e., lies on) both those lines", which is the property described above.
		All it means is that it logically consistent for there to be concepts called "points" and "lines" that satisfy the axioms of geometry with the projective axiom in place of the parallel postulate.
		In summary, then, projective geometry can be thought of as the study of points and "lines" (great circles) on a surface obtained by gluing the equator of a hemisphere to itself.
	www.math.toronto.edu /mathnet/questionCorner/projective.html (2444 words)

	HSU Research Forum (HRF) :: True Subwoofers and Home Theater - View Single Post - "customizing surround ...
		I just purchased my first HT setup which consists of axiom speakers and an hsu sub.
		I need to place the rear surrounds on the fireplace mantle, but they have down firing woofers.
		I bought some 7/8 wood dowels which i thought of cutting to size and gluing to the speakers, than I was going to put either plastic caps or felt on the bottom.
	www.hsuresearch.com /forum/showpost.php?p=6292&postcount=1 (126 words)

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