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Topic: Inverse limit

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Direct limit

Limit (category theory)

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	Inverse
		Inverse-square law - The magnitude of a force is proportional to the inverse square of the distance.
		Inverse gamblers fallacy - It says that if something improbable happens now, probable events must have happened in the past or the future.
		Inverse (logic) - ~p → ~q is the inverse of p → q
	www.ebroadcast.com.au /lookup/encyclopedia/in/Inverse.html (183 words)

	PlanetMath: categorical direct product is an inverse limit
		It is then clear that the universal property of an inverse limit is equivalent to the universal property defining a categorical direct product.
		These results are of interest when one is looking to prove exactness of sums and products in a category: often it is easier to address exactness of direct and inverse limits, and the result then applies to many other constructions as well.
		This is version 1 of categorical direct product is an inverse limit, born on 2004-02-25.
	planetmath.org /encyclopedia/CategoricalDirectProductIsAnInverseLimit.html (197 words)

	Inverse limit - Education - Information - Educational Resources - Encyclopedia - Music
		In mathematics, the inverse limit (also called the projective limit) is a construction which allows one to "glue together" several related objects, the precise matter of the gluing process being specified by morphisms between the objects.
		Inverse limits can be defined in any category, but we will initially only consider inverse limits of groups.
		The categorical dual of an inverse limit is a direct limit (or inductive limit).
	www.music.us /education/I/Inverse-limit.htm (807 words)

	PlanetMath: direct limit (Site not responding. Last check: 2007-09-10)
		Occasionally, the inverse limit is also called the projective limit or simply the limit.
		This universal property is the most generally useful characterization of the inverse limit.
		This is version 7 of direct limit, born on 2004-02-24, modified 2006-08-22.
	planetmath.org /encyclopedia/Limit2.html (395 words)

	Direct Limit, Inverse Limit
		The limit of this diagram, if it exists, is called the inverse limit, or the projective limit.
		To explore the inverse limit, let's move to the category of topological spaces and continuous functions.
		Therefore f is continuous, and q is the inverse limit.
	www.mathreference.com /cat,dirlim.html (1015 words)

	Limit (category theory) - Wikipedia, the free encyclopedia
		Limits and colimits have strong relationships to the categorial concepts of universal morphisms and adjoint functors.
		The dual notion of limits and cones are colimits and co-cones.
		Limits for a diagram D: J → X are said to be created by a functor F: X → Y if every limit cone of F o D has a unique pre-image cone under F in X, and additionally this unique pre-image is a limit cone of D.
	en.wikipedia.org /wiki/Limit_(category_theory) (1993 words)

	P-adic number
		A definite meaning is given to these sums based on Cauchy sequences using the p-adic metric[?].
		Note that pointwise addition and multiplication of such sequences is well defined, since addition and multiplication commute with the mod operator, see modular arithmetic.
		The reals and the p-adic numbers are the completions of the rationals; it is also possible to complete other fields, for instance general algebraic number fields, in an analogous way.
	www.ebroadcast.com.au /lookup/encyclopedia/p-/P-adic_number.html (1234 words)

	Springer Online Reference Works
		-modules are examples of inverse limits in their respective categories.
		The concept of an inverse limit is a categorical generalization of the topological concept of a projective limit.
		There is a competing terminology, with  "direct limit" replaced by "colimit" , and "inverse limit" by "limit" .
	eom.springer.de /s/s091930.htm (136 words)

	Orbits of turning points for maps of finite graphs and inverse limit spaces by Brian Raines (Site not responding. Last check: 2007-09-10)
		In this paper we examine the topology of inverse limit spaces generated by maps of finite graphs.
		We show that if f has finitely many turning points each on a finite orbit then the inverse limit of f is determined by the number of elements in the \omega-limit set of each turning point.
		We go on to identify the local structure of the inverse limit space at the points that correspond to points in the \omega-limit set of f when the turning points of f are not necessarily on a finite orbit.
	www.univie.ac.at /EMIS/proceedings/TopoSym2001/24.htm (173 words)

	PlanetMath: inverse limit
		The concept of inverse limit can be defined in far more generality.
		For a good example of this more general construction, see infinite Galois theory.
		This is version 7 of inverse limit, born on 2003-08-26, modified 2005-10-08.
	planetmath.org /encyclopedia/InverseLimit2.html (172 words)

	[No title]
		The Homology of Homotopy Inverse Limits by Paul G. Goerss1 Abstract: The homology of a homotopy inverse limit can be studied by a spec* tral sequence with has E2 term the derived functors of limit* in the category of coal* *gebras.
		One of the standard problems in homotopy theory is to calculate the homolog* y of a given type of inverse* limit.
		Derived functors of limits in the category of coalgebras Let CA be the category of graded cocommutative coalgebras over a field k.
	www.math.purdue.edu /research/atopology/Goerss/limits.txt (10037 words)

	Planar Embeddings of Inverse Limit Spaces of Unimodal Maps - Bruin (ResearchIndex)
		2 A symbolic representation of inverse limit spaces for a clas..
		1 Embedding inverse limits of interval maps as attractors (context) - Misiurewicz - 1985
		1 Inverse limits of certain interval mappings as attractor in..
	citeseer.ist.psu.edu /475235.html (499 words)

	Projectile Motion with Resistance and the Lambert W Function -- from Mathematica Information Center
		We also give a partial solution to the inverse problem of finding the elevation angles that give rise to given range values by obtaining a closed form for the angle generating the maximum range in terms of the initial velocity and the resistance constant.
		To do this we develop a general theorem, which may be of interest in its own right, about inverse functions arising from real-analytic functions.
		A second issue relates to the newly emerging area of Experimental Mathematics (Borwein and Corless [2]) and raises practical and philosophical questions about the use of symbolic computation to "discover" new results and the extent to which such computation can be viewed as an accepted form of proof.
	library.wolfram.com /infocenter/Articles/6226 (373 words)

	Subcontinua of Inverse Limit Spaces of Unimodal Maps (ResearchIndex)
		Based on the combinatorial properties of the unimodal maps, properties of the subcontinua of the inverse limit spaces are studied.
		Among other results, we give combinatorial conditions for an inverse limit space to have only arc+ray subcontinua as proper (nontrivial) subcontinua.
		Also maps are constructed whose inverse limit spaces have the inverse limit spaces of a prescribed set of periodic unimodal...
	citeseer.ist.psu.edu /488322.html (532 words)

	ProFunds: Inverse ProFunds (Site not responding. Last check: 2007-09-10)
		Inverse ProFunds seek to increase in value when the market declines and decrease in value when the market rises—a result that is the opposite of traditional mutual funds.
		ProFunds does not limit how often an investor may exchange among ProFunds and does not impose transaction fee when investors buy, sell or exchange a ProFund (excluding a $10 wire redemption fee imposed under certain circumstances).
		Lipper defines ''inverse funds'' as an open-end mutual fund (not an Exchange Traded Fund, or ETF) that seeks investment results corresponding to the inverse (opposite) of the performance of an assigned index.
	www.profunds.com /profiles/inverse.asp (348 words)

	[No title] (Site not responding. Last check: 2007-09-10)
		Profinite groups are inverse limits of finite groups.
		Because the inverse limit can be constructed as a subset of a certain product, it inherits a topology from the product topology.
		Perhaps surprisingly this topology is nontrivial: in fact, the inverse limit of finite groups is compact, Hausdorff, and totally disconnected (every point is its own connected component).
	www.math.washington.edu /~rosoff/sas/abstracts.html (492 words)

	Stalks and Direct Limits
		The limit is then an object in the image category, call it L, with maps FROM each of the vertices such that whenever you have a--->b in the diagram the composition of a to L is the same as a to b then b to L WHEN IT EXISTS.
		In this category, the inverse limit of C is the empty set (right?).
		The inverse limit doesn't exist (there is no reason to suppose limits must exist), that is different.
	www.physicsforums.com /showthread.php?p=243906 (1955 words)

	TIP201
		This method of transient protection is the simplest, and at the same time the most limited, SCRs and diodes are selected to have a certain minimum PIV rating, which is "guess-timated" to be sufficient to allow them to withstand the transient spikes to which they may be subjected.
		The limiting factor to any suppression scheme is the total energy rating of the MOVs used to shunt the transient spikes.
		Clamping ensures that the inverse voltages impressed on a semiconductor will never exceed a pre-determined level, and that the semiconductors themselves carry the full energy of a shunted transient spike.
	www.payneng.com /tip201.htm (847 words)

	InVerse Scripture Memorization learning Bible verses freeware (Site not responding. Last check: 2007-09-10)
		InVerse simplifies this, containing over 15,300+ verses preloaded in 2,800 of the best known Bible passages from 11 Bible translations.
		Inverse lets you choose whether to see just the reference (e.g.
		If you want a better sense of the meaning, a quick mouse click will show the context as it appears in the Bible, with verses that come before and/or after.
	www.bibleinverse.org (252 words)

	Atlas: Subcontinua of Fibonacci-like Inverse Limit Spaces by Henk Bruin (Site not responding. Last check: 2007-09-10)
		Inverse limit spaces of unimodal maps have been suggested as a model for global attractors of non-uniformly hyperbolic dynamical systems.
		The classification of such inverse limit spaces has been carried out for unimodal maps with a finite critical orbit, but little is known when the critical orbit is infinite.
		In this talk I will present general sufficient condition for a Fibonacci-like inverse limit space to have only sin 1/x curves as non-trivial subcontinua, and discuss some crude way of classifying the inverse limit spaces using these subcontinua.
	atlas-conferences.com /cgi-bin/abstract/casx-17 (166 words)

	Citebase - A monomorphism theorem for the inverse limit of nested retracts (Site not responding. Last check: 2007-09-10)
		Citebase - A monomorphism theorem for the inverse limit of nested retracts
		A monomorphism theorem for the inverse limit of nested retracts
		Various characterizations are offered of injectivity of the canonical fundamental group homomorphism for a certain class of inverse limit spaces.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0502275 (115 words)

	Math 583GA: homework
		Due Wedneday, 9 April: let p be a prime number, and describe the inverse limit (a.k.a.
		When I say "describe", I mean that, ideally, you should relate these to familiar groups and/or rings (for some value of the word "familiar").
		Answer: the inverse limit is isomorphic to the p-adics.
	www.math.washington.edu /~palmieri/Courses/2002/Math583/old-homework.html (629 words)

	[No title]
		Now a Hom into a projective limit is the same as a compatible set of Hom's into each term, so the sequence of Hom's into projective limit is exact if the sequence for each term is exact.
		(4.3.2) "The inductive limit of stalks of sheaves = stalk of the inductive limit of sheaves." Reason: stalks are themselves direct limits, so this basically uses the fact that inductive limits commute.
		I guess that the point is that direct sum is a special case of direct limits, and so the sheaf direct sum is not the same as the presheaf direct sum.
	math.stanford.edu /~vakil/ega0 (5238 words)

	Cauchy sequence - Article from FactBug.org - the fast Wikipedia mirror site (Site not responding. Last check: 2007-09-10)
		They are of interest because in a complete space, all such sequences converge to a limit, and one can test for "Cauchiness" without knowing the value of the limit (if it exists), in contrast to the definition of convergence.
		A metric space X in which every Cauchy sequence has a limit (in X) is called complete.
		The values of the exponential, sine and cosine functions, exp(x), sin(x), cos(x), are irrational for any rational value of x≠0, but are defined as limit of a rational sequence which is their Maclaurin series.
	www.factbug.org /cgi-bin/a.cgi?a=6085 (598 words)

	Citebase - Orbits of turning points for maps of finite graphs and inverse limit spaces (Site not responding. Last check: 2007-09-10)
		Orbits of turning points for maps of finite graphs and inverse limit spaces
		We show that if f has finitely many turning points each on a finite orbit then the inverse limit of f is determined by the number of elements in the ω-limit set of each turning point.
		We go on to identify the local structure of the inverse limit space at the points that correspond to points in the ω-limit set of f when the turning points of f are not necessarily on a finite orbit.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/0204137 (217 words)

	No Title (Site not responding. Last check: 2007-09-10)
		We work within the one parameter family of symmetric tent maps, where the slope is the parameter.
		with periodic turning points of the same period, we use the finite kneading sequences of the maps to obtain a necessary condition for the inverse limit spaces
		It is known that if the periods differ, then the inverse limit spaces are not homeomorphic.
	www.uwm.edu /~gb/COLLOQUIA/99-03-29/99-03-29.html (116 words)

	NSDL Metadata Record -- kernel is an inverse limit
		This is exactly the universal condition for a kernel in an abelian category.
		By reversing arrows, we can see that a cokernel is a direct limit.
		This result can be extremely useful in proving exactness results: one shows that finite inverse and direct limits exist and are exact in a particular category, and one immediately obtains the fact that sums, products, kernels and cokernels are all exact.
	nsdl.org /mr/1035239 (111 words)

	AMCA: Topological classification of inverse limit spaces of tent maps with finite critical orbit by Sonja Stimac (Site not responding. Last check: 2007-09-10)
		AMCA: Topological classification of inverse limit spaces of tent maps with finite critical orbit by Sonja Stimac
		Topological classification of inverse limit spaces of tent maps with finite critical orbit
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/m/r/85.htm (163 words)

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