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Topic: Hilbert cube

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	Hilbert cube - Wikipedia, the free encyclopedia
		Topologically, the Hilbert cube may be defined as the product of countably infinitely many copies of the unit interval [0,1].
		That is, it is the cube of countably infinite dimension.
		But the Hilbert cube fails to be a neighbourhood of any point p because its side becomes smaller and smaller in each dimension, so that an open ball around p of any fixed radius e > 0 must go outside the cube in some dimension.
	en.wikipedia.org /wiki/Hilbert_cube (280 words)

	Search Results for Hilbert (Site not responding. Last check: 2007-10-22)
		Hilbert's seventh problem asked for a proof of the transcendence of a to the power b when a is an algebraic number and b is an irrational algebraic number.
		Hilbert in 1900 posed the problem of finding a method for solving Diophantine equations as the 10th problem on his famous list of 23 problems which he believed should be the major challenges for mathematical research this century.
		Hilbert, Hurwitz and Lindemann all lectured to Sommerfeld and, after attending a course by Hilbert on the theory of ideal numbers, he felt that abstract pure mathematics was the right subject for him.
	www-groups.dcs.st-and.ac.uk /history/Search/historysearch.cgi?SUGGESTION=Hilbert&CONTEXT=1 (11603 words)

	Locally compact space - Wikipedia, the free encyclopedia
		The first two examples show that a subset of a locally compact space need not be locally compact, which contrasts with the open and closed subsets in the previous section.
		This example also contrasts with the Hilbert cube as an example of a compact space; there is no contradiction because the cube cannot be a neighbourhood of any point in Hilbert space.
		As mentioned in the previous section, any compact Hausdorff space is also locally compact, and any locally compact Hausdorff space is in fact a Tychonoff space.
	en.wikipedia.org /wiki/Locally_compact (1342 words)

	Cornell Math - James E. West
		An example of the interplay between these theories is that manifolds modeled on the Hilbert cube appear naturally in several ways as limits of stabilization processes for finite-dimensional objects, and, unlike standard function space stabilization, retain more of their important properties, e.g.
		Study of the Hilbert cube manifolds has produced several of the initial breakthroughs in introducing control into the homeomorphism theory of finite-dimensional manifolds.
		This in turn, has been useful in analyzing the failure of the classical matrix algebra to describe equivariant homeomorphisms and homotopy types of manifolds with locally linearizable transformation groups, which in turn has led to new results on the topological classification of linear representations of finite groups.
	www.math.cornell.edu /People/Faculty/westj.html (207 words)

	[No title]
		If the cube "wraps around" on each face then these tetrahedra are joined in pairs along the faces which were part of the cube.
		Hilbert's third problem (H3P) began as a problem in the foundation of geometry: Show that there is no "elementary" geometric theory of volume for Euclidean polyhedra, as against the existence of such a theory for area.
		ISBN 0-273-08426-7 The third Hilbert problem was solved (in a negative sense) by Dehn a few months after its formulation but this result generates a new problem: to find a complete system of invariants of a polyhedron with respect to scissors congruence.
	www.math.niu.edu /~rusin/known-math/98/sydler (5088 words)

	Koders - quantize.c
		Color allocation is % defined over a domain consisting of the cube in RGB space with opposite % vertices at (0,0,0) and (cmax,cmax,cmax).
		In the following discussion % these cubes are defined by the coordinate of two opposite vertices: % The vertex nearest the origin in RGB space and the vertex farthest from % the origin.
		Each lower level in the tree is generated by % subdividing one node's cube into eight smaller cubes of equal size.
	www.koders.com /c/fid87D12CA3FE27422CC7503732CE708D54C3A8900D.aspx (1597 words)

	hyperspace
		Schori and J. West, "The hyperspace of the closed unit interval is a Hilbert cube", Trans.
		Curtis and R. Schori, "Hyperspaces of Peano Continua are Hilbert cubes", Fund.
		Torunczyk, "On CE-images of the Hilbert cube and characterization of Q-manifolds" Fund.
	www.spsu.edu /math/stricklen/Hyperspace/hyperspace.htm (1827 words)

	A Cube-filling Hilbert Curve (Site not responding. Last check: 2007-10-22)
		In 1891 David Hilbert gave a simple construction of a Peano curve whose limit filled a square.
		In constructing one iterate from the previous one, note that the direction of the curve determines the orientation of the smaller cubes inside the larger one.
		The initial stage of this three dimensional curve can be considered as coming from the 3-bit reflected Gray code which traverses the 3-digit binary strings in such a way that each string differs from its predecessor in a single position by the addition or subtraction of 1.
	www.math.uwaterloo.ca /~wgilbert/Research/HilbertCurve/HilbertCurve.html (198 words)

	Research (Site not responding. Last check: 2007-10-22)
		In fact, this is extactly what we do when we define and construct a partial cube.
		In the second case, our objective is to reduce the storage footprint of the views that will actually be constructed.
		Though compression algorithms are quite common in the literature, most are poorly suited to database/cube environments since they (i) offer relatively poor compression ratios or (ii) result in significant run-time penalties.
	www.cs.concordia.ca /~eavis/research7.html (144 words)

	Control And Relaxation Over The Circle - Hughes, Prassidis (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		7 Lectures on Hilbert cube manifolds (context) - Chapman - 1976
		1 Approximate fibrations and bundle maps on Hilbert cube manif..
		1 Concordances of Hilbert cube manifolds (context) - Chapman - 1976
	citeseer.ist.psu.edu /hughes00control.html (784 words)

	Hilbert - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "Hilbert" is defined.
		Hilbert : Columbia Gazetteer of North America [home, info]
		Phrases that include Hilbert: hilbert space, david hilbert, hilbert basis theorem, hilbert cube, hilbert david, more...
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=Hilbert (107 words)

	Topology (Site not responding. Last check: 2007-10-22)
		Major part of my research concerned topological properties of infinite-dimensional spaces, such as the Hilbert cube or Banach spaces.
		Toruńczyk, Homeomorphism groups of compact Hlbert cube manifolds which are manifolds, Bull.
		Toruńczyk (with J. West), Fibrations and bundles with Hilbert cube manifold fibers, Mem.
	www.impan.gov.pl /About/topology.html (1054 words)

	Topological Equivalence Of Discontinuous Norms (ResearchIndex)
		0, h maps the Hilbert cube [\Gammar; r] N precisely onto the "elliptic cube" fx 2 R N : P 1 i=1 jx i j p r p g.
		This means that the supremum norm and for instance the Hilbert norm (p = 2) are topologically indistinguishable as functions on R N.
		4 Hilbert space is homeomorphic to the countable infinite prod..
	citeseer.ist.psu.edu /474620.html (252 words)

	View topic - [SPEC] Where is Perplex City?
		Ok, first, remember the cube is from a prerunner civilization, as Sente and media reports stated.
		Basically it was a math equation to form a cube containing infinite mass, or indeterminate mass.
		The academy actually had the cube in their possession or at least according to our notes they did.
	forums.unfiction.com /forums/viewtopic.php?p=134578 (1273 words)

	Abstracts for publications and preprints of J. T. Tyson
		Schori and West proved that $K([0,1])$ is homeomorphic with the Hilbert cube, while Hohti showed that $K([0,1])$ is not bi-Lipschitz equivalent with a variety of metric Hilbert cubes.
		We reduce the problem to the verification of a capacity estimate in domains satisfing a quasihyperbolic boundary condition, which we establish using a combination of a chaining argument involving the Poincaré inequality on Whitney cubes together with Frostman's theorem.
		We also discuss related results where the quasihyperbolic boundary condition is slightly weakened; in this case the Hölder continuity of quasiconformal maps is replaced by uniform continuity with a modulus of continuity which we calculate explicitly.
	www.math.uiuc.edu /~tyson/abstracts.html (2307 words)

	Margie Hale's Education (Site not responding. Last check: 2007-10-22)
		The dissertation deals with the topology of some direct limit spaces and their related homeomorphism groups.
		In particular, let R denote the real numbers and Q the Hilbert cube.
		Qualifying paper: Two Theorems from Hilbert Cube Manifold Theory.
	www.stetson.edu /~mhale/vita/educat.htm (254 words)

	Fourier Analysis (MATH 520, Spring 2001)
		(The ``cube'' of sidelength L is, of course, the set of all vectors, whose all coordinates are real numbers between 0 and L. The volume is L^N, where L is the sidelength, and N the dimension.)
		Notice that this cube (of dimension two billion) is much ``smaller'' than the cube of the same sidelength in an infinite-dimensional Hilbert space; if placed inside, it will be almost imperceptible.
		It is easy to draw a good picture (a parallel projection into the plane) of a 3-dimensional cube.
	www.math.purdue.edu /~eremenko/520.html (1025 words)

	MASS - Colloquia 2003
		(Hilbert's 3rd problem)" ABSTRACT: A similar question for polygons has an affirmative answer: given two polygonal domains of the same area, one can cut the first one into polygonal pieces and to assemble the second one.
		In dimension three, however, it is not true: the answer to the question in the title is "no"!
		This theorem which provides an answer to one of the famous Hilbert's problems was proved by Max Dehn (actually, a year before Hilbert stated his Problems).
	www.math.psu.edu /mass/colloquia/2003 (1031 words)

	Knowledge Creation as a Square Dance on the Hilbert Cube
		Knowledge Creation as a Square Dance on the Hilbert Cube
		"Knowledge Creation as a Square Dance on the Hilbert Cube," Econometric Society 2004 North American Summer Meetings 204, Econometric Society.
		Authors registered on the RePEc Author Service receive monthly emails with details about downloads and abstract views of their works.
	ideas.repec.org /p/wpa/wuwpga/0401004.html (596 words)

	Hilbert Curve Notes (Site not responding. Last check: 2007-10-22)
		This cube-filling Hilbert curve was also produced independently by
		Manipulation and presentation of multidimensional image data using the Peano scan.
		Here is an ASCII text-graphic of the cube-filling Hilbert curve that was posted to the FRAC-L fractal discussion list.
	www.math.uwaterloo.ca /~wgilbert/Research/HilbertCurve/HilbertCurveNotes.html (88 words)

	References for IMR 2004
		He will not tell you about Hilbert cube manifolds and homology manifolds unless you ask.
		The hilbert polynomial of a graded module carries a lot of information about the algebra.
		We will have a look at the coefficients of the the hilbert polynomial and attempt to extract some information from them.
	www.math.rutgers.edu /grad/IMR/comments_2004.html (2222 words)

	UCL > The Department of Mathematics > Research
		Is it consistent that the covering of the Hilbert cube requires more Cantor sets than that of the interval?
		Is every Borel mapping of a metric space X to a metric space Y of bounded class?
		Are the ball and the sphere of the Hilbert space Lipschitz isomorphic?
	www.ucl.ac.uk /math/staff/MC.html (165 words)

	Atlas: The Topological Weak Rohlin Property and Topological Entropy by Eli Glasner (Site not responding. Last check: 2007-10-22)
		The group G acts on itself by conjugation and we say that X satisfies the topological weak Rholin property if this action has dense orbits.
		We show that both the Hilbert cube and the Cantor set satisfy this property.
		We also show that zero entropy is generic for homeomorphisms of the Cantor set, whereas it is infinite entropy which is generic for homeomorphisms of the Hilbert cube.
	atlas-conferences.com /cgi-bin/abstract/cadp-02 (154 words)

	[No title] (Site not responding. Last check: 2007-10-22)
		Abstract:In our note, we prove the result that the Hilbert's cube equipped with \newline $l_p-$metrics, $p\ge 1$, cannot be isometrically embedded into $c$.
		Abstract:I discuss the number of iterations of the elementary sequential closure operation required to achieve the full sequential closure of a set in spaces of the form $C_p(X)$.
		Abstract:We present a forcing construction of a Hausdorff zero-dimensional Lindel\"of space $X$ whose square $X^2$ is again Lindel\"of but its cube $X^3$ has a closed discrete subspace of size ${\frak c}^+$, hence the Lindel\"of degree $L(X^3) = {\frak c}^+ $.
	www.maths.tcd.ie /EMIS/journals/CMUC/cmuc9402/abstrall.htm (1374 words)

	EDUCATION AND PUBLICATIONS FOR VO LIEM (Site not responding. Last check: 2007-10-22)
		Infinite products which are homeomorphic to Hilbert space, with D.W. Curtis, Gen. Top.
		Concordance classes of free actions of compact Lie groups on infinite- dimensional manifolds, Proc.
		Some results on semi-free actions of finite groups on Hilbert cube manifolds, Top.
	www.math.ua.edu /~vliem/vitae.htm (254 words)

	Research Interests (Technical version) (Site not responding. Last check: 2007-10-22)
		I maintain a strong interest in 4-manifold topology, and hope to get back to some problems in that area soon.
		Infinite dimensional (Hilbert cube) manifolds play a role in some of my recent work.
		However, the largest part of my research has involved high dimensional manifolds.
	www.uwm.edu /People/craigg/researcht.html (234 words)

	ipedia.com: Compact space Article (Site not responding. Last check: 2007-10-22)
		This construction can be performed for any finite set, not just {0, 1}.
		The spectrum of any continuous linear operator on a Hilbert space is a compact subset of C.
		The spectrum of any commutative ring or Boolean algebra is compact.
	www.ipedia.com /compact_space.html (1389 words)

	1
		Bestvina, P. Bowers, J. Mogilski and J. Walsh, Characterization of Hilbert space manifolds revisited, Topology and Appl.
		Dobrowolski and J. Mogilski, Absorbing sets in the Hilbert cube related to transfinite dimension, Bull.
		J.J. Dijkstra and J. Mogilski, The topological product structure of systems of Lebesque spaces, Math.
	blue.utb.edu /jkm/publications.htm (432 words)

	Atlas: West's problem on equivariant hyperspaces and the Banach-Mazur compacta by Sergey Antonyan (Site not responding. Last check: 2007-10-22)
		In 1976 J. West asked the following question: Let G be a compact connected Lie group.
		Whether the orbit space (exp G)/G is an absolute retract, and if so, whether it is always homeomorphic to the Hilbert cube?
		On this way we discover new properties of the Banach-Mazur compacta, for instance, we prove that the complement BM (n) of the unique singular point in BM(n) is a Hilbert cube manifold for every n
	atlas-conferences.com /cgi-bin/abstract/caje-70 (178 words)

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