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Topic: Uniform isomorphism

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	Uniform space - Wikipedia, the free encyclopedia
		Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and uniform convergence.
		Uniform spaces may be defined alternatively and equivalently using systems of pseudometrics, an approach which is often useful in functional analysis.
		Every uniform space is a completely regular topological space, and conversely, every completely regular space can be turned into a uniform space (often in many ways) so that the induced topology coincides with the given one.
	en.wikipedia.org /wiki/Uniform_space (1583 words)

	Homeomorphism - Wikipedia, the free encyclopedia
		In the mathematical field of topology a homeomorphism or topological isomorphism (from the Greek words homeos = identical and morphe = shape) is a special isomorphism between topological spaces which respects topological properties.
		Every uniform isomorphism and isometric isomorphism is a homeomorphism.
		uniform isomorphism is an isomorphism between uniform spaces
	en.wikipedia.org /wiki/Homeomorphism (708 words)

	FINDING OUT ABOUT FILLING IN: A GUIDE TO PERCEPTUAL COMPLETION FOR VISUAL SCIENCE AND THE PHILOSOPHY OF PERCEPTION
		Furthermore, the isomorphism is typically taken to hold for spatial or topographic properties, thus suggesting that vision involves representations having the form of an "internal screen" or "scale model" that preserves the metric properties of the external world (O'Regan 1992).
		Isomorphism in Köhler's sense can be seen as a particular instance of the Analogy idea, one in which "looks like" is taken in the sense of structural correspondence.
		The doctrine of analytic isomorphism states that it is a condition on the adequacy of cognitive neuroscientific explanation that there be an ultimate neural foundation where an isomorphism obtains between neural activity and the subject's experience.
	www.bbsonline.org /Preprints/OldArchive/bbs.pessoa.html (19981 words)

	An Introduction to Banach Space Theory
		Section 5.3 is devoted to generalizations of uniform rotundity, and discusses local uniform rotundity, weak uniform rotundity, weak* uniform rotundity, weak local uniform rotundity, strong rotundity, and midpoint local uniform rotundity, as well as the relationships between these properties.
		Uniform smoothness is the subject of the next section, in which the property is defined using the modulus of smoothness and characterized in terms of the uniform Frechet differentiability of the norm.
		Frechet smoothness and uniform Gateaux smoothness are examined in the final section of the chapter, and Smulian's results on the duality between these properties and various generalizations of uniform rotundity are obtained.
	www.math.lsa.umich.edu /~meggin/ibst.html (2897 words)

	Lotus Artificial Life - Isomorphic automata (Site not responding. Last check: 2007-11-06)
		The isomorphism can be seen relatively easily by super-imposing the differing grids the automata work on, and looking at cells overlapping one sublattice of the triangular automaton.
		A similar isomorphism demonstrably exists between the Margolus neighbourhood and one of the two alternating sub-lattices generated by the 16-state rectangular scheme of Morita and Ueno.
		There are also isomorphisms between the X neighbourhood and the 16-state rectangular scheme of Morita and Ueno, and between the Y neighbourhood and the 8-state triangular scheme of Morita and Ueno.
	www.alife.co.uk /ca/relationship (390 words)

	Gestalt Isomorphism (Site not responding. Last check: 2007-11-06)
		Isomorphism differs subtly from MÜLLER's axiom in that it states explicitly what is only implied by MÜLLER, that in the case of structured experience, equal dimensionality between percept and representation implies similarity of structure or form (KÖHLER 1947, p.
		In particular, all of these representations have a problem with encoding multiple surfaces at different depths, as in the perception of transparency, or encoding the volume of empty space that is perceived between the observer and a visible surface.
		For example images containing large regions of uniform brightness can be encoded in terms of the contrast along the edges bounding those regions, from which the brightness of the region can be reconstructed when necessary.
	cns-alumni.bu.edu /pub/slehar/webstuff/isomorph/isomorph.html (6846 words)

	Phenomenology naturalized (Site not responding. Last check: 2007-11-06)
		The filling-in controversy is not only empirical, however, for it involves fundamental conceptual and methodological issues about the proper form of explanation in visual science, as well as deeper philosophical issues about the nature of visual perception, issues especially familiar to philosophers and psychologists in the phenomenological tradition.
		As we discussed in Section 1, it is this assumption of spatial isomorphism that typically lies behind the appeal to neural filling-in in visual science.
		Visual scientists are mistaken when they interpret the evidence for neural filling-in within the framework of analytic isomorphism, but Dennett is equally mistaken when he says that talk of filling-in reveals a commitment to Cartesian materialism.
	people.ucsc.edu /~anoe/completion.html (13746 words)

	Part 1
		Although nauty is generally considered to be the fastest algorithm for solving the isomorphism problem it has been shown that it does not work well for all types of graphs [3].
		However, it should be noted that the time spent in solving the isomorphism is quite less than the time it takes to generate the graphs.
		It is not until we enter the large graphs that we actually see a uniform increase in running time with respect to the number of vertices.
	www.cs.rice.edu /~qasem/projects/graphis.html (1732 words)

	Weak and strong normalization, $\mathbf{K}$-redexes, and first-order logic (Site not responding. Last check: 2007-11-06)
		Uniform normalisation means that the term can either not be reduced to a normal form, or that all ways of reducing the term will eventually lead to a normal form.
		The reason for the indistinctness in the formulation of the conservation theorem is that Lambda I is closed under beta-reduction, which in Lambda I does not erase subterms.
		This uniformly normalising subset is used to infer strong normalisation from weak normalisation for Lambda M. This is a non-trivial extension of techniques developed recently by Sørensen and Xi to infer strong normalisation from weak normalisation of the same notion of reduction.
	www.linearity.org /turtle/reports/Neergaard-WSNK-1999.html (428 words)

	Paper's Abstract
		Uniformity of space filling is the most important and essential feature of the uniform design.
		UNIFORM DESIGN METHOD illustrated in this article is the result of special need of China at the time, China's emphasis on basic theory research, Professor Wang Yuan and Fang Kai-Tai have high research level in this field, and cooperation of the scientists and engineer of CASC.
		Uniform design is superior to orthogonal design and optimality design in their table's usage.
	www.math.hkbu.edu.hk /UniformDesign/abstract.html (6688 words)

	Homeomorphic [Definition] (Site not responding. Last check: 2007-11-06)
		In the mathematical field of topology a homeomorphism or topological isomorphism (from the Greek The Greek language (Greek Ελληνικά, IPA // – "Hellenic") is an Indo-European language with a documented history of some 3,000 years.
		Every uniform isomorphism In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces which respects uniform properties....
		diffeomorphism In mathematics, a diffeomorphism is a kind of isomorphism of smooth manifolds.
	www.wikimirror.com /Homeomorphic (1225 words)

	Homeomorphism [Definition] (Site not responding. Last check: 2007-11-06)
		[click for more] a homeomorphism or topological isomorphism (from the Greek words homeos = identical and morphe = shape) is a special isomorphism between topological spaces Topological spaces are structures that allow one to formalize concepts such as convergence, connectedness and continuity.
		An outstanding use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology....
		uniform isomorphism In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces which respects uniform properties....
	www.wikimirror.com /Homeomorphism (1628 words)

	scoutscanada.ca - Uniform isomorphism (Site not responding. Last check: 2007-11-06)
		Uniform Isomorphism - Information In Free Online Encyclopedia: TheFreeDictionary.c...
		In the mathematical field of topology a uniform isomorphism or uniform homeomorphism is a special isomorphism between uniform spaces which respects uniform properties.
		A function f between two uniform spaces X and Y is called uniform isomorphism if it satisfies the following properties
	72evg.scoutscanada.ca /Uniform-isomorphism/reference/fullview/wikipedia/1344480 (116 words)

	NASSLLI 2002 (Site not responding. Last check: 2007-11-06)
		This is the Curry-Howard Isomorphism between typed lambda-terms and intuitionistic deductions.
		A discovery of a natural system of self-referential proof terms, which we call "proof polynomials", was essential in recent solution to the famous open problem of Goedel (1933) concerning formalization of provability.
		Proof polynomials considerably extend the Curry-Howard Isomorphism and lead to a joint calculus of propositions and proofs which unifies modal and epistemic logic with combinatory logic and typed lambda-calculus.
	www.stanford.edu /group/nasslli/courses/Proof.htm (328 words)

	uniform_space (Site not responding. Last check: 2007-11-06)
		A uniform space is a set U equipped with a nonempty collection Î¦ of subsets of the Cartesian product X Ã— X...
		UNIFORM SPACE DENSITY Â Â Â In our first example the light pulse was passed through a crystal that remained...
		The uniform discretization is shown in Figure 1.
	uniform_space.networklive.org (325 words)

	Theory Seminars at CMU SCS '96-'97
		Isomorphism Theorem: The sets complete under AC^0 reductions are all isomorphic under isomorphisms computable and invertible by AC^0 circuits of depth three.
		This Gap Theorem does not hold for strongly uniform reductions: there are sets complete for NC^1 under Dlogtime-uniform AC^0 reductions that are not complete under Dlogtime-uniform NC^0 reductions.
		The main tool is a theorem that shows that any Sigma^2_3 circuit on n variables that accepts A inputs and has size s must be constant on a projection (subset defined by equations of the form x_i=0, x_i=1, x_i=x_j or x_i=\bar{x}_j) of dimension at least log(A/s)/(log n).
	www.cs.cmu.edu /~theoryseminar/Previous_Years/theoryseminar96-97.html (3379 words)

	Associative binary Operators
		We say that a uniform binary operator (A×Ag:A) left-associates over a binary operator (A×Bf:B) precisely if, for every a, c in A and b in B: f(g(a,c),b)=f(a,f(c,b)).
		We have just shown that Known(1): the bulk action on a direct sum is the result of combining the bulk actions of its constituents with f whenever the right-hand constituent's domain has at most one member.
		We then have natural isomorphisms equating p=n+(p\q), q=n+(q\p) and u=(q\p)+n+(p\q), whence n+u is isomorphic to n+(q\p)+n+(p\q) which is, in turn, isomorphic to p+q.
	www.chaos.org.uk /~eddy/math/associate.html (3337 words)

	Credits (Site not responding. Last check: 2007-11-06)
		This Curry-Howard isomorphism was used by N. de Bruijn in the Automath project, the first full-scale attempt to develop and mechanically verify mathematical proofs.
		Exploiting this Curry-Howard isomorphism, notable achievements in proof theory saw the emergence of two type-theoretic frameworks; the first one, Martin-Löf's Intuitionistic Theory of Types, attempts a new foundation of mathematics on constructive principles.
		The purpose here is a better uniformity making the tactics and commands easier to use and to remember.
	pauillac.inria.fr /coq/doc/Reference-Manual002.html (3075 words)

	Volume 24, Number 1, 1998
		The main result: every free monoid is isomorphic to the monoid of all nonconstant continuous selfmaps of a metrizable co-connected space.
		We present the original proof, based on the Doitchinov completion, that a totally bounded quiet quasi-uniformity is a uniformity.
		In particular it follows from Künzi's [8] proofs that each totally bounded locally quiet quasi-uniform space is uniform, and recently Déak [10] observed that even each totally bounded Cauchy quasi-uniformity is a uniformity.
	www.math.bas.bg /~serdica/n1_98.html (1138 words)

	Volume 23, Number 3-4, 1997
		Let K be a field of characteristic p>0 and let G be a direct sum of cyclic groups, such that its torsion part is a p -group.
		If a Banach space E cannot be decomposed into a direct sum of separable and reflexive subspaces, then there exists a normed space Z and a linear continuous bijective operator T:E\to Z such that T^{-1} is not a Borel map.
		It is shown that the dual unit ball B_{X^} of a Banach space X^ in its weak star topology is a uniform Eberlein compact if and only if X admits a uniformly G\^ateaux smooth norm and X is a subspace of a weakly compactly generated space.
	www.math.bas.bg /~serdica/n34_97.html (1166 words)

	Uniform space - Enpsychlopedia (Site not responding. Last check: 2007-11-06)
		Every topological group ( G,⋅) (in particular, every topological vector space) becomes a uniform space if we define a subset V of G × G to be an entourage if and only if it contains the set { ( x, y) : x ⋅ y
		This uniform structure on G is called the right uniformity on G, because for every a in G, the right multiplication x → x ⋅ a is uniformly continuous with respect to this uniform structure.
		-space if and only if the intersection of all the elements of its uniform structure equals the diagonal {( x, x) : x in X }.
	www.grohol.com /psypsych/Uniform_space (1627 words)

	/usr/local/etc/httpd/htdocs/archive/sem_coll_2000
		The construction is based on the existence of a canonical isomorphism between the skein algebra of the torus and the subalgebra of the noncommutative torus generated by noncommutative cosines.
		Finally we describe a combinatorial analogue of the Ihara-Selberg zeta function of a uniform lattice L in G ; this relates the "length spectrum" to the spectrum of the combinatorial Laplacian on L\X.
		We identify functional derivatives that play the role of non-classical temperature and non-classical chemical potentials and show that these potentials are uniform at equilibrium in the absence of external forces.
	www.math.buffalo.edu /archive/sem_coll_2000.html (6995 words)

	Research
		Among other things, this paper shows that the isomorphism relation on complex surfaces is essentially countable but not essentially hyperfinite -- this is in contrast to the isomorphism relation on higher dimensional complex manifolds, which is not essentially countable.
		A dichotomy for isomorphism (or the latex file, or the ps file).
		A Borel isomorphism relation is either essentially countable or as complicated as the countably infinite product of the Vitali equivalence relation.
	www.math.ucla.edu /~greg/research.html (1579 words)

	Master-/Dimploma Thesis of Phuong Nguyen (Site not responding. Last check: 2007-11-06)
		We introduce a finitely axiomatizable second-order theory VTC^0 and show that it characterizes precisely the class uniform TC^0.
		Finally, we show that VTC^0 is RSUV isomorphic to the first-order theory \Delta-CR, which has been claimed the ``minimal'' theory for TC^0 by Johannsen and Pollett.
		This isomorphism shows that VTC^0 admits the \Sigma_{0^+}^B(\Delta_1^B) comprehension rule.
	www.eccc.uni-trier.de /eccc-local/ECCC-Theses/nguyen.html (129 words)

	ECCC Report TR04-008 and related Papers (Site not responding. Last check: 2007-11-06)
		Abstract: The Group Isomorphism problem consists in deciding whether two input groups $G_1$ and $G_2$ given by their multiplication tables are isomorphic.
		We derandomize this protocol begin{itemize} item[(a)] When the input groups are solvable, we give a uniform NP machine for Group Non-Isomorphism, that works correctly on all but $2^{{rm polylog}(n)}$ inputs of any length $n$.
		We also show that the hardness of Group Isomorphism for the parameterized class W[1] would have a similar unlikely consequence for $overline{clique}$.
	www.eccc.uni-trier.de /eccc-reports/2004/TR04-008 (293 words)

	scoutscanada.ca - Webelos Uniform (Site not responding. Last check: 2007-11-06)
		Point out the three special parts of the Webelos Scout uniform.
		Tell when to wear the uniform and when not to wear it.
		[ Webelos Requirements ] [ Webelos Resources ] [ Webelos Uniform ] WEBELOS is an acronym that stands for "WE'll BE LOyal Scouts!".
	72evg.scoutscanada.ca /Webelos-Uniform/reference/search (46 words)

	Concurrency Abstracts (Site not responding. Last check: 2007-11-06)
		We prove full completeness for a fragment of the linear logic of the self-dual monoidal category of Chu spaces over 2, namely that the proofs between semisimple (conjunctive normal form) formulas of multiplicative linear logic without constants having two occurrences of each variable are in bijection with the dinatural transformations between the corresponding functors.
		We give a uniform representation of the objects of mathematical practice as Chu spaces, forming a concrete self-dual bicomplete closed category and hence a constructive model of linear logic.
		The motivating application is a uniform theory of abstract or parametrized time in which to any given notion of time there corresponds an algebra of concurrent behaviors and their operations, always the same operations but interpreted automatically and appropriately for that notion of time.
	boole.stanford.edu /abstracts.html (9685 words)

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