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Topic: Bohr compactification

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	Bohr compactification - Wikipedia, the free encyclopedia
		In mathematics, the Bohr compactification of a topological group G is a compact Hausdorff topological group H that may be canonically associated to G.
		The Bohr compactification is intimately connected to the finite-dimensional unitary representation theory of a topological group.
		The Bohr compactification also reduces many problems in the theory of almost periodic functions on topological groups to that of functions on compact groups.
	en.wikipedia.org /wiki/Bohr_compactification (336 words)

	Compactification (mathematics) - Wikipedia, the free encyclopedia
		The methods of compactification are various, but each is a way of controlling points from "going off to infinity" by in some way adding "points at infinity" or preventing such an "escape".
		An embedding of a topological space X as a dense subset of a compact space is called a compactification of X. Embeddings into compact Hausdorff spaces may be of particular interest.
		The Bohr compactification of a topological group arises from the consideration of almost periodic functions.
	en.wikipedia.org /wiki/Compactification_(mathematics) (1102 words)

	[No title]
		By a group compactification I meant the initial homomorphism G->bG from a discrete group G to a compact group bG such that the image of G is dense in bG.
		The compactification map is not required to be a homeomorphism onto its image.
		If bG is the one-point compactification of G then G embeds in bG but the action of G on bG fixes the point at "infinity" hence the group structure does not extend to bG.
	www.math.niu.edu /~rusin/known-math/99/compactification_grp (1216 words)

	AMCA: Bohr compactifications of topological algebraic structures and almost periodic functions by Salvador Hernandez
		The Bohr compactification is a well known construction for (topological) groups and semigroups.
		In this case, the Bohr compactification is defined as the maximal compactification which is compatible with the structure involved.
		Thus, the Bohr compactification of any (topological) algebraic structure is characterized as the Gelfand space associated to the commutative Banach algebra of all almost periodic functions what has been the initial definition for groups and semigroups.
	at.yorku.ca /c/a/k/b/20.htm (216 words)

	Compactification (Site not responding. Last check: 2007-10-24)
		The methods of compactification are various, but each is a way of controlling points from ''going off to infinity'' by in some way reifying a limit into a point or points, or preventing such an ''escape''.
		As I understand it, the Bohr compactification can be defined using either only Hausdorff compact groups (what some people simply refer to simply as compact groups) or quasi-compact groups (what some other people refer to simply as compact groups, unfortunately).
		The mechanism behind this type of compactification is described by the Kaluza-Klein theory.
	www.wwwtln.com /finance/41/compactification.html (1097 words)

	Research interests: Hugo Junghenn (Site not responding. Last check: 2007-10-24)
		The subject has its origins in the work of H. Bohr in the beginning of this century on almost periodic functions on the real line.
		The unifying concept in the study of these diverse areas is the right topological semigroup compactification.
		The algebraic structure of this compactification plays an essential role in determining the functional analytic properties of representations of the underlying semigroup, the analytical properties of functions on semigroups, and the topological dynamical properties of actions of the semigroup on compact spaces.
	www.gwu.edu /~math/research/junghenn.html (209 words)

	Department web - University Jaume I
		A characterization of the Schur property by means of the Bohr topology.
		The concept of boundedness and the Bohr compactification of a MAP Abelian Group.
		The dimension of a LCA Group in its bohr topology.
	www.mat.uji.es /persona/index2pubi.php?p_per_id=65370 (168 words)

	BIOINFORMATICS<-->STRUCTURE Abstract:Bohr (Site not responding. Last check: 2007-10-24)
		Structural fold classes for proteins are being represented on a three dimensional lattice and a model Hamiltonian[1] is suggested that can explain the division into fold classes during the compactification stage of the folding process.
		Proteins are described by chains of secondary structure elements with hinges in between, being the important degree of freedom.
		We have performed a statistical analysis of available protein structures and found agreement with the predicted preferred abundances of proteins with a magic number of secondary structures.
	www.weizmann.ac.il /home/jsgrp/pdb25sp10/abstracts/Bohr.html (265 words)

	Springer Online Reference Works
		A unified account of the theory of almost-periodic functions on groups can also be found in [a2] and [a3], Sect.
		is isomorphic to the Banach algebra of all continuous functions on the so-called Bohr compactification
		In this way the theory is reduced to the theory of continuous functions on a compact group (e.g., the mean-value theorem corresponds to the normalized Haar measure on
	eom.springer.de /a/a011980.htm (745 words)

	Bohr bug Definition / Bohr bug Research (Site not responding. Last check: 2007-10-24)
		Bohr bug is a term used in softwareComputer software (or simply software) refers to one or further computer programs and data held in the storage of a computer for some purpose.
		Program software performs the function of the program it implements, either by directly providing instructions to the computer hardware or by serving as input to another piece of software.
		Bohr bug is a nasty but well defined thing.
	www.elresearch.com /Bohr_bug (161 words)

	Re: *-algebras and quantization
		> > > >Do you know the variant of this trick that gives the Bohr > >compactification of R? > I think it is the algebra generated by the imaginary exponentials f(x) > = exp (ikx) for all real k.
		You do have to be careful because the Bohr compactification is not a 'true' compactification.
		The topology as a subset of the Stone-Cech compactification is the same as the usual topology.
	www.lns.cornell.edu /spr/2003-08/msg0053450.html (135 words)

	Atlas: The Concept of Boundedness and the Bohr Compactification of a MAP Abelian Group by Jorge Galindo (Site not responding. Last check: 2007-10-24)
		Atlas: The Concept of Boundedness and the Bohr Compactification of a MAP Abelian Group by Jorge Galindo
		and the Bohr topology of G for some well known groups with boundedness (G, obtaining some uniform boundedness results which generalize classical theorems such as Glicksberg's theorem on weakly compact subsets of a LCA group and the uniform boundedness principle on a locally convex vector space.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caah-20.
	atlas-conferences.com /c/a/a/h/20.htm (187 words)

	J. Galindo's recent publications (Site not responding. Last check: 2007-10-24)
		Totally bounded group topologies that are Bohr topologies of LCA groups.
		The concept of boundedness and the Bohr compactification of a MAP abelian group, Fundamenta Mathematicae 159 (1999), no. 3, 195--218.
		A characterization of the Schur property by means of the Bohr topology, Topology and Its Applications 97 (1999), no. 1-2, 99--108.
	www3.uji.es /~jgalindo/publications.html (178 words)

	AMCA: The concept of boundedness and the Bohr compactification of a MAP Abelian group by Salvador Hernandez (Site not responding. Last check: 2007-10-24)
		AMCA: The concept of boundedness and the Bohr compactification of a MAP Abelian group by Salvador Hernandez
		Let G be a MAP Abelian group and let \Cal B be a boundedness in the sense of Vilenkin.
		We study the relations between \Cal B and the Bohr topology of G for some well known groups with boundedness (G, \Cal B), obtaining some uniform boundedness results which generalize classical theorems such as Glicksberg's theorem on weakly compact subsets of a LCA group and the uniform boundedness principle on a locally convex vector space.
	at.yorku.ca /c/a/a/g/02.htm (181 words)

	Math Forum Discussions
		> conditions the dual is called the Bohr compactification of Q. Is this
		Bohr compactification: for an abelian group G with locally compact
		Starting with the group Q, ((Q,Dis)^,Dis)^ is the Bohr compactification
	mathforum.org /kb/thread.jspa?threadID=1157093&messageID=3792768 (170 words)

	R&E 24 Abstracts
		We comment here on some recent results and problems for the most part related to the Bohr compactification and Bohr topology of an arbitrary topological group.
		Our principal goal is to summarize some of the recent progress concerning the Bohr topology of a topological group.
		Accordingly, we begin with a brief discussion of the Bohr topology on a discrete Abelian group.
	www.heldermann.de /R&E/rae24abs.htm (1668 words)

	[No title]
		By the universal property of the Stone-Cech compactification, for the inclusion map f: X \subset I, and since Y is compact Hausdorff, there exists a map q:BX \to Y such that the composition of the natural map X \to BX followed by q coincides with f.
		In this case (at least) BX is called the Stone-Cech compactification of X.
		The solenoid group (which can be defined in various ways, for example as the inverse limit of the family of coverings of the circle, ordered by divisibility) is maybe the most interesting example.
	www.lehigh.edu /~dmd1/yr1013.txt (1401 words)

	[No title] (Site not responding. Last check: 2007-10-24)
		It turns out that not every set of positive density in $Z^3$ has a similar property, namely, there are large sets in $Z^3$ which DO NOT contain a Cartesian cube $B \ times B \ times B$ with $B$ having positive upper density in $Z$.
		This is related to the subtle distinction between topological and measurable recurrence and some new results about Bohr neighborhoods of 0 in $Z$.
		The talk should be accessible to graduate students.
	www.math.technion.ac.il /~techm/20011218143020011218ber (117 words)

	5.2 Isotropy
		A well-known example is the one point compactification, which is the spectrum of the algebra of continuous functions
		In the present case, the procedure is more complicated and leads to the Bohr compactification
		It is very different from the one point compactification, as can be seen from the fact that the only function which is continuous on both spaces is the zero function.
	relativity.livingreviews.org /Articles/lrr-2005-11/articlesu25.html (868 words)

	Abstract Harmonic Analysis Research Group
		Filali and P. Salmi, Slowly oscillating functions in semigroup compactifications and convolution algebras, 2006 (submitted).
		Tomi Alaste, Perfect Semigroups and The Bohr Compactification of Conoids, Licenciate Thesis 2006, (PDF / PS).
		Pekka Salmi, The Set of Idempotents is Not Closed in the Weakly Almost Periodic Compactification of Integers, Licenciate Thesis 2003, (PDF).
	cc.oulu.fi /~harmonic/publications.html (472 words)

	Journal of Lie Theory, Vol. 14, No. 1, pp. 73--109, 2004 (Site not responding. Last check: 2007-10-24)
		Abstract: Using the tools introduced in [Breckner, B. E., and W. Ruppert, J. Lie Theory 11 (2001), 559--604], we investigate topological semigroup compactifications of closed connected submonoids with dense interior of Sl(2,R).
		In particular, we show that the growth of such a compactification is always contained in the minimal ideal, and describe the subspace of all minimal idempotents (typically a two-cell) and the maximal subgroups (these are always isomorphic with a compactification of R).
		For a large class of such semigroups we give explicit constructions yielding all possible topological semigroup compactifications and determine the structure of the compactification lattice.
	www.univie.ac.at /EMIS/journals/JLT/vol.14_no.1/2.html (146 words)

	[No title] (Site not responding. Last check: 2007-10-24)
		In these field theories, the field operators are almost periodic functions of the space coordinate $x$.
		There is a natural notion of a mean in the theory of almost periodic functions, the Bohr mean, which plays the role of the integral.
		This $\bC^$-algebra can be identified with the $\bC^$-algebra of continuous functions on the following Bohr compactification of $\bR$.
	www.ma.utexas.edu /mp_arc/papers/96-355 (3671 words)

	recent developments in LQG
		Start with a space that isnt compact, make a ring of functions that are well behaved on it in some fashion, take the maximal ideals, with some topology and it may turn out to be a compact space "including" the original.
		Ashtekar used that method of compactification in a cosmology paper recently calling it "the Bohr compactification of the real line".
		I couldn't remember having heard of the Bohr compactification before but I harbor a deep suspicion that maximal ideals were being used there too.
	www.physicsforums.com /showthread.php?mode=hybrid&t=4399 (3068 words)

	[No title]
		This compactification is a quantum group version of the Bohr compactification of topological groups.
		In case of discrete quantum groups there is a more explicit description of this compactification and it yields new examples of compact quantum groups.
		Taking an advantage of the concept of a factor state and the Weak Stone Weierstrass Theorem, we prove a general criterion on the fiber product of -algebras to be dense in the fiber product of their C-completions.
	www.impan.gov.pl /~pmh/seminar/sem04.html (3359 words)

	Fourier Analysis on Groups by Walter Rudin (Site not responding. Last check: 2007-10-24)
		Also, there are classical subjects which lead almost inevitably to this extension of the theory.
		For instance, Bohr (1) noticed almost 50 years ago that the unique factorization theorem for positive integers allows us to regard every ordinary Dirichlet series as a power series in infinitely many variables.
		The boundary values yield a function of infinitely many variables, periodic in each, that is to say, a function on the infinite-dimensional torus T
	www.apronus.com /math/fouriergroups.htm (677 words)

	Citebase - van Douwen's problems related to the Bohr topology
		van Douwen's problems related to the Bohr topology
		We comment van Douwen's problems on the Bohr topology of the abelian groups raised in his paper (The maximal totally bounded group topology on G and the biggest minimal G-space for Abelian groups G) as well as the steps in the solution of some of them.
		New solutions to two of the resolved problems are also given.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0204120 (138 words)

	[No title]
		The Bohr compactification and the Bohr topology for groups are well-known in harmonic analysis, but in fact, these notions easily generalize to arbitrary structures.
		A surprising number of results can be proved in this general setting.
		In this talk, we define the basic notions, discuss some general results, and then look at what is known for specific structures, such as groups and lattices.
	www.math.ohiou.edu /~qvu/seminars/98-99/hart.html (63 words)

	papers
		Let $G$ be an infinite, connected, planar graph with bounded vertex degree, which obeys a strong isoperimetric inequality and which can be embedded in the plane so that each cycle surrounds only finitely many vertices.
		We investigate a certain class of compactifications of $G$; one of which has boundary homeomorphic to a circle.
		Although the distribution may be written in terms of asymptotic densities (actual computation of which may be difficult) we may also express it in terms of i.i.d.
	faculty.plattsburgh.edu /sam.northshield/papers.htm (1791 words)

	Re: *-algebras and quantization
		The spectrum of this algebra is the Stone-Cech compactification of R, more or less by definition.
		The Stone-Cech compactification is the "biggest possible" one, while the one-point compactification is the "smallest possible" one.
		Do you know the variant of this trick that gives the Bohr compactification of R? How about the 2-point compactification of R (= the closed unit interval)?
	www.lns.cornell.edu /spr/2003-08/msg0053275.html (248 words)

	Research
		Suitable sets in products of topological groups and in groups equipped with the Bohr topology
		Relating a locally compact Abelian group to its Bohr compactification
		The Bohr compactification, modulo a metrizable subgroup, (with W.~W. Comfort and T.-S. Wu), Fund.
	www.csubak.edu /~jtrigos/research/research.htm (446 words)

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