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Topic: Topological structure

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	Topological vector space - Wikipedia, the free encyclopedia
		As the name suggests the space blends a topological structure (a uniform structure to be precise) with the algebraic concept of a vector space.
		The elements of topological vector spaces are typically functions, and the topology is often defined so as to capture a particular notion of convergence of sequences of functions.
		A topological vector space X is a vector space over a topological field K (most often the real or complex numbers with their standard topologies) which is endowed with a topology such that vector addition X × X → X and scalar multiplication K × X → X are continuous functions.
	en.wikipedia.org /wiki/Topological_vector_space (1113 words)

	Topology (via CobWeb/3.1 planetlab2.netlab.uky.edu) (Site not responding. Last check: 2007-10-16)
		Topology is concerned with the study of the so-called topological properties of figures, that is to say properties that do not change under bicontinuous one-to-one transformations (called homeomorphisms).
		The traditional joke is that the topologist can't tell the coffee cup she is drinking out of from the donut she is eating, since a sufficiently pliable donut could be reshaped to the form of a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle.
		In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures defined on arbitrary categories which allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories.
	topology.iqnaut.net.cob-web.org:8888 (1336 words)

	[No title] (Site not responding. Last check: 2007-10-16)
		By proposition 2.3, the coproduct (and Hopf algebra structure) on the E2-term E2*(R) = HH(H(R; Fp)) that is derived from the R-Hopf algebra structure* on 16 VIGLEIK ANGELTVEIT AND JOHN ROGNES T HH(R) agrees with the algebraically defined structure on the Hochschild homol- ogy HH() of the commutative algebra = H(R; Fp).
		The A-comodule structure* is given on H(ko; F2) by restricting the coproduct on A, and on the algebra gene* *ra- tors by (oe,~41) = 1 oe,~41and (oe,~22)= 1 oe,~22+ ~,21 oe,~41 (oe,~3)= 1 oe,~3+ ~,1 oe,~22+ ~,2 oe,~41.
		The A-comodule structure* is given on H(tmf; F2) by restricting the coproduct on A, and on the algebra generators by (oe,~81) = 1 oe,~81and (oe,~42)= 1 oe,~42+ ~,41 oe,~81 (oe,~23)= 1 oe,~23+ ~,21 oe,~42+ ~,22 oe,~81 (oe,~4)= 1 oe,~4+ ~,1 oe,~23+ ~,2 oe,~42+ ~,3 oe,~81.
	www.math.purdue.edu /research/atopology/Angeltveit-Rognes/vigleik.txt (12372 words)

	Topology Perdu
		If structure is presupposed given as a concept and defined in a mathematical theory, then topology is one structure among others: group structures, vector space structure, manifold structure, etc. — and the conjunction of topology and psychoanalysis is a metaphor.
		Lacanian psychoanalysis disengages this natural observation in the formation of a structural concept: the obstacle between a theory of the individual and the milieu (the group, society, culture, etc.), between the part and the whole, is resolved by a seemingly innocuous move founded on a definition of structure exemplified in Cantor's set theory.
		Psychoanalytically, these problems can be used to landmark the emergence of structure in the topological isolation of the individual: the milieu (whole) is equivalent to the individual (part) as an oddly interior exteriority, thus making the problem of the individuation and the relation to an object particularly delicate.
	topoi.net /place6/topologyperdu.html (3233 words)

	Topology
		The second, geometric topology, focuses on the connectivity properties of topological spaces and provides the core results from general topology that serve as background for subsequent courses in geometry and algebraic topology.
		In fact, point like structure of g fuzzy set is a kind of behaviour of their level structures, or in other words, stratifications.
		Although the peculiar level structures of fuzzy topological spaces makes some problems complicated, however, it is just level structure itself which makes fuzzy topological spaces possesses more abundant properties, making the relation between fuzzy topology and other branches of classical mathematics closer.
	www.wordtrade.com /science/mathematics/topology.htm (2132 words)

	PlanetMath: manifold
		A differential manifold is a topological manifold with some additional structure information.
		The topological hypotheses in the definition of a manifold are needed to exclude certain counter-intuitive pathologies.
		Standard illustrations of these pathologies are given by the long line (lack of paracompactness) and the forked line (points cannot be separated).
	planetmath.org /encyclopedia/DifferentialStructure.html (350 words)

	Perceiving topological structure of 2-D patterns (Site not responding. Last check: 2007-10-16)
		I investigated observers' sensitivity to the topological structure of visual stimuli.
		Three factors were taken to capture the topological structure of 2-D patterns: The number of disconnected components, the number of holes (connections), and inclusion relationships.
		If studied in isolation, any given topological property is typically confounded with the presence of particular features such as line terminations and contour length, or with Gestalt principles of perceptual organization.
	vision.arc.nasa.gov /AFH/Seminars/sem06-09-99.html (168 words)

	“ON THE MATHEMATICAL FORMULATION OF A TOPOLOGICAL MODEL FOR THE STRUCTURE OF ELMENTARY PARTICLES OF PHYSICS ACCORDING ...
		A topological model for the structure of elementary particles is proposed.
		Topological particles from which matter is to be created fill the space-time and are to be the building blocks of space-time.
		There are only two kinds of elementary particles being the building blocks of space-time: the first one, whose topological structure has positive gaussian curvature and the second one whose topological structure has negative gaussian curvature.
	www.space-time-mass.com /totalpaper.htm (1187 words)

	convergence spaces (Site not responding. Last check: 2007-10-16)
		Convergence spaces are for topological spaces like complex numbers are for real numbers; where some topological problems fail to find their solutions in topologies, they will, however, in convergences.
		Every topological property in a given row is preserved by the class of maps of this row (or of a higher row).
		The class of sequential topological spaces is of particular interest, on one hand because it is exactly the class of spaces for which sequences suffice to describe the topology, on the other hand because this is exactly the class of topological quotient of metrizable spaces.
	www.cs.georgiasouthern.edu /faculty/mynard_f/convergences.htm (3488 words)

	Topological condensate concept
		One ends up with the concept of the topological condensate from the requirement that both TGD as a Poincare invariant gravity and TGD as generalization of the string model pictures make sense as appropriate limiting cases.
		Topological condensate has a hierarchical structure and one can associate a characteristic length scale spesifying the minimum size of the 3-surfaces on each level of the hierarchy.
		This picture of topological condensate is consistent with the general properties of the Kähler action.
	www.physics.helsinki.fi /~matpitka/topcond.html (487 words)

	Introduction
		A physicist's ``dynamical quest'' consists of first dissecting the topological form of a strange set, and second, ``dressing'' this topological form with its metric structure.
		Topological signatures and ergodic measures usually present different aspects of the same dynamical system, though there are some unifying principles between the two approaches, which can often be found via symbolic dynamics [11].
		Topological invariants, on the other hand, can be stable under parameter changes and therefore are useful in identifying the same dynamical system at different parameter values.
	cnls.lanl.gov /People/nbt/Book/node136.html (1149 words)

	Research in the Topological Fluid Dynamics Group
		In the latter the magnetic structure breaks up and re-connects, a process often accompanied by explosive eruptions where enormous amounts of energy are set free.
		The storage and release of magnetic energy in complex field structures is also important for the dynamo theory, which investigates the origin and dynamics of magnetic fields in planets and stars.
		This is suggested by a certain analogy in the underlying mathematical structure and represents an extraordinary, most interesting and new approach to the understanding of electromagnetic fields.
	www.tp4.ruhr-uni-bochum.de /vw/project.html (966 words)

	I depart from the fact in observing a piece of matter and taking into account the following ordinary fact:
		There are no gaps between our topological particles since it is assumed that it is impossible to talk of a mathematical empty space in physics.
		3.3 On the gaussian curvature and topological structure.
		According to my theory, photons must be the result of topological changes successively (say, particles that have not experimented compactification processes properly) which is the manifestation of their movement.
	www.space-time-mass.com /technicalpaper.htm (1056 words)

	Topological domain structure of the Escherichia coli chromosome -- Postow et al. 18 (14): 1766 -- Genes and Development
		Bliska, J.B. and Cozzarelli, N.R. Use of site-specific recombination as a probe of DNA structure and metabolism in vivo.
		Lynch, A.S. and Wang, J.C. Anchoring of DNA to the bacterial cytoplasmic membrane through cotranscriptional synthesis of polypeptides encoding membrane proteins or proteins for export: A mechanism of plasmid hypernegative supercoiling in mutants deficient in DNA topoisomerase I. Bacteriol.
		Worcel, A. and Burgi, E. On the structure of the folded chromosome of Escherichia coli.
	www.genesdev.org /cgi/content/full/18/14/1766 (8184 words)

	NMR Solution Structure and Topological Orientation of Monomeric Phospholamban in Dodecylphosphocholine Micelles -- ...
		To probe the topological orientation of PLB in detergent micelles,
		This is not the case for the structure in organic solvent (B and D).
		Structure of the 1–36 amino-terminal fragment of human phospholamban by nuclear magnetic resonance and modeling of the phospholamban pentamer.
	www.biophysj.org /cgi/content/full/85/4/2589 (4852 words)

	AMCA: Locally topological groupoids and extendibility by Osman Mucuk
		The topological structure of W does not in general extend to a topological groupoid structure on G which restricts to that on W, but there is a topological groupoid H called the holonomy groupoid with a morphism H --> G such that H contains W as a subspace and H has a universal property.
		A locally topological groupoid (G, W) is called extendible if there is a topology on G such that G is a topological groupoid with this topology and W is open in G. A locally topological groupoid is not in general extendible.
		In this paper we prove that if G is a locally sectionable topological groupoid and W is an open subset containing all the identities, then using the criterion obtained from the holonomy, the monodromy groupoid MG gives rise to a locally topological groupoid (MG, W) which is extendible.
	at.yorku.ca /c/a/g/x/44.htm (460 words)

	An Atlas of Cyberspaces - Topology Maps
		The underlying data on the topological structure of the Internet is gathered by skitter, a CAIDA tool for large-scale collection and analysis of Internet traffic path data.
		Netscan is an ambitious project analysing the social structure of Usenet news.
		The example opposite is a screenshot of the Crosspost Visualization tool of Netscan which enables you to analyse the connections between newsgroups.
	www.cybergeography.org /atlas/topology.html (668 words)

	ORDER STRUCTURE AND TOPOLOGICAL METHODS IN NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
		The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis.
		This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems.
		The maximum principle is revisited through the use of the Krein—Rutman theorem and the principal eigenvalues.
	www.worldscibooks.com /mathematics/5999.html (283 words)

	Topological structure analysis of the protein-protein interaction network in budding yeast -- Bu et al. 31 (9): 2443 -- ... (Site not responding. Last check: 2007-10-16)
		Topological structure analysis of the protein-protein interaction network in budding yeast -- Bu et al.
		Topological structure analysis of the protein–protein interaction network in budding yeast
		The spectral analysis revealed a hidden topological structure underlying the miscellaneous network (b).
	nar.oxfordjournals.org /cgi/content/full/31/9/2443 (3055 words)

	Topological Geometrodynamics
		The metric, conformal and symplectic structures of the light cone boundary
		Infinite primes and the structure of many-sheeted space-time
		II factors and the spinor structure of infinite-dimensional configuration space of 3-surfaces
	www.helsinki.fi /~matpitka/tgd.html (3343 words)

	Elsevier MDL :: Solutions :: White Papers :: Modeling Blood-Brain Barrier Partitioning Using Topological Structure ...
		Development of a QSAR model for drug blood-brain barrier partitioning is a challenging problem, approached in this study with the use of topological molecular structure representation.
		A QSAR model is developed for in vivo blood-brain partitioning data treated as the logarithm of the blood-brain concentration ratio.
		Further, a clustering of the data on the structure descriptors reveals the relationship between structure and the logBB values.
	www.mdli.com /solutions/white_papers/MDLQSARreprint.jsp (199 words)

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