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Topic: Relative topology

	United States Patent Application: 0020111761
		For example, relative values of properties may be relative density or concentration of ore derived from core samples of mineral deposits in geological analysis.
		Relative values for scalar properties of these systems and the space in which they exist can be obtained via any suitable means, as are well known in the art.
		The implementation of the eigenvector following method during the examination of the topology of the density facilitates the location of all critical points and allowing the tracing of the connections between the peaks in the density (peptide fragments) to be traced.
	appft1.uspto.gov /netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PG01&p=1&u=/netahtml/PTO/srchnum.html&r=1&f=G&l=50&s1='20020111761'.PGNR.&OS=DN/20020111761&RS=DN/20020111761 (10439 words)

	What's Going On with the Topology of Recursion
		The topology of the torus is found to be ubiquitous where recursions and invariants are concerned.
		As a mathematical discipline, topology can be and usually is encrypted into rather incomprehensible symbolic formulations, but where authors such as Firby or Barr condescend to illustrate their texts and relate the findings of topologists to visualizable embodiments, even the layman can glean some benefits.
		The “topology of biology” is not a typical undergraduate course, but it is surely not the worst subject matter to reconsider early and often.
	www.library.utoronto.ca /see/SEED/Vol4-1/McNeil.htm (8392 words)

	PlanetMath: subspace topology (Site not responding. Last check: 2007-11-07)
		is the topology whose open sets are those subsets of
		obtained by taking the subspace topology is called a topological subspace, or simply subspace, of
		This is version 3 of subspace topology, born on 2001-10-25, modified 2003-03-13.
	planetmath.org /encyclopedia/SubspaceTopology.html (45 words)

	Protein topology literature
		Although the diagrams did not imply any formal definition of protein topology and were not generated automatically, they were found to be a very valuable aid to understanding protein folds and their similarities and differences at the topological level.
		Diagrams representing the topology of the beta sheets were introduced along with a notation describing the topological connectivity of the sheets as a string of numbers,letters and symbols.
		Several definitions of "contact" were tested, the main application being not comparison of topology for database searches but rather what insights into the folding process and domain organization of the proteins could be gained by considering the connectivity of the graphs under various definitions and strength thresholds for the helical contacts.
	www3.ebi.ac.uk /tops/Literature.html (4051 words)

	Coelomata and Not Ecdysozoa: Evidence From Genome-Wide Phylogenetic Analysis -- Wolf et al. 14 (1): 29 -- Genome ...
		The effect of relative branch lengths of tree topology.
		Err-simC, fraction of wrong topologies (error rate) for the trees reconstructed from alignments simulated by using model trees with the coelomate topology.
		Horizontal axis: the length of the nematode branch relative to the human branch.
	www.genome.org /cgi/content/full/14/1/29 (5357 words)

	Time Travel [Internet Encyclopedia of Philosophy] (Site not responding. Last check: 2007-11-07)
		The fundamental principle in General Relativity is the equivalence principle, which states that gravity and acceleration are two names designating the same phenomenon.
		If you are accelerating upwards at a rate g in an elevator located in a region of spacetime without a gravitational field, the force you would feel and the motion of objects in the elevator with you would be indistinguishable from an elevator that is stationary within a downward uniform gravitational field of magnitude g.
		So far, we are not aware of any solution to General Relativity that describes the evolution of a CTC in a spacetime region where time travel had not been possible previously; however, it is usually assumed that there are such solutions to the equations.
	www.iep.utm.edu /t/timetravel.htm (7833 words)

	Relative Compactness from the Bitopological Point of View (Site not responding. Last check: 2007-11-07)
		The notion of relative compactness based on the relation of two topologies on the same set and used by Z. Balogh instead of the above-mentioned idea clearly reveals, even at first glance, the bitopological essence of this notion.
		Thus we are able to choose different kinds of bitopological local compactness leading to the relative compactness.
		Besides, the strengthening of relative compactness makes it possible to connect the resulting strong compactness with a special type local compactness by the equivalence relation.
	www.pmf.ukim.edu.mk /mathematics/dvalishvili.htm (294 words)

	definitions (Site not responding. Last check: 2007-11-07)
		Hence, two particles which have relative motion will always have (with respect to one another) antiparallel velocities since their motions are not taken with respect to a coordinate system but only with respect to each other.
		For example, from the viewpoint of either of two quantum particles which have relative motion one must consider that either the viewpoint quantum is moving or the other quantum is moving.
		Such topology makes a neutron the source of a time gradient field (gravity field) because it is an example of a special type of homeomorphism wherein the source velocity potentials which comprise the inner torus (electron) are mapped onto and one to one with the sink velocity potentials of the outer torus (proton).
	www.singtech.com /definitions.html (4781 words)

	[No title]
		Despite this, the relative homotopy groups ßn(X, A, x) were found to be in * general non- abelian for n = 2, and as a result J.H.C. Whitehead in the 1940s introduced the * term `crossed module' for the properties of the boundary map @ : ß2(X, A, x) !
		It therefore seemed a good idea for us to * look at the relative* situation in dimension 2, that is, to start from a based pair X* = (X,* * A, C), where C is a set of base points, and define a homotopy double groupoid æ(X) using maps * of squares.
		Nonabelian Algebraic Topology * * 4 _________________________________
	hopf.math.purdue.edu /BrownR/IMA-talk.txt (3300 words)

	MPtopo Download
		Membrane Protein Topology Database Listing generated on Tue Aug 09 10:01:02 PDT 2005 Created by Sajith Jayasinghe, Kalina Hristova, Stephen White Managed and maintained by Michael Myers and Craig Snider Copyright (c) 2000-2005 by its creators.
		Relative to Swiss-Prot, the first several hundred residues are missing from the PDB sequence.
		Tet(K) (S. aureus) file_name:tet-k.txt entry_date:3may99 refman_number:16910 author:Hirata,T., Fujihira,E., Kimura-Someya,T., Yamaguchi,A. (1998) [Membrane topology of the Staphylococcal tetracycline efflux protein Tet(K) determined by antibacterial resistance gene fusion] {J Biochem, 124, 1206-1211} remarks:Sequence is from PIR, which is the same as sequence used in the reference cited.
	blanco.biomol.uci.edu /mptopo/mptopodownload.html (6824 words)

	[No title]
		] A subset of a topological space is relatively closed if it is a closed set in some relative topology of a subset.
		] A subset of a topological space is relatively open if it is an open set in some relative topology of a subset.
		The nonquantum mechanics of a system of particles or of a fluid interacting with an electromagnetic field, in the case when some of the velocities are comparable with the speed of light.
	www.accessscience.com /Dictionary/R/R16/DictR16.html (2415 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		For $k=0,1,\dots, \infty$, the topologies $\tau^k_N$ are known as the {\sl Whitney $k$-topologies}.
		In this paper a topology on $\Gammainf E$ is always induced from a topology on $\Cinf N E$.
		For the last statement it suffices to observe that for $f$ to be a limit of a sequence $\family f n$ in the topology $\TC$ it is only required that the sequence $\set{j^kf_n}_n$ converge $d_k$- uniformly to $j^kf$ on any compact subset of $N$ for all $k$.
	home.imf.au.dk /esn/preprints/025 (11860 words)

	PRG Research Report RR-03-07
		We show that a measurement &mu on a continuous dcpo D extends to a measurement μ on the convex powerdomain C D iff it is a Lebesgue measurement.
		In particular, ker &mu must be metrizable in its relative Scott topology.
		Moreover, the space ker μ in its relative Scott topology is homeomorphic to the Vietoris hyperspace of ker &mu, i.e., the space of nonempty compact subsets of ker &mu in its Vietoris topology -- the topology induced by any Hausdorff metric.
	web.comlab.ox.ac.uk /oucl/publications/tr/rr-03-07.html (165 words)

	» Introduction to Topology
		However, I think this can leave a student with a narrow view of topology, as the definition for a topology is abstract and doesn't depend on the discussion of metric spaces.
		I read Introduction to Topology in three stages: as a review of set theory and metric spaces (chapters 1 and 2), then as an introduction to topology (chapter 3), and lastly as a detailed look at two important topological properties, connectedness (chapter 4) and compactness (chapter 5).
		If you have not had the luxury of taking a topology course during your undergraduate studies, but you need to know some topology and you have to study it by yourself, this is the book you need.
	www.mathreading.com /Shop/Introduction-to-Topology/0486663523 (1058 words)

	User talk:Trovatore - Wikipedia, the free encyclopedia
		I changed it to "subspace" because that seemed to me like the more common and more likely to be understood term, especially by the general reader.
		In my experience all three terms are (or were) common, but It has been many years since I was a practicing topologist (or mathematician for that matter), so I may be unfamiliar with current usage.
		Are you saying that you think "relative" is more usual in the context of the Baire space, or in general?
	en.wikipedia.org /wiki/User_talk:Trovatore (1898 words)

	Time: Hitoshi Kitada's Home Page
		At the stage of general theory of relativity, the field equation with the invariance postulate with respect to diffeomorphisms requires one to eliminate the size of the frames in which clocks reside.
		It seems that this problem may be avoided by an interpretation that the general theory of relativity is an approximation of reality, and the theory gives a sufficiently good approximation as experiments and astronomical observations show.
		Now we are in a position to give a solution of unifying quantum mechanics (QM) and classical mechanics (CM) governed by special theory of relativity, which I have arrived at on February 15, 2001, whose precise formulation is given in time IX paper.
	www.kitada.com (7069 words)

	No Title
		Being open for the finite-complement topology, V is a complement of a finite set.
		-open sets, which are not open in the finite-complement topology (say, non-empty open intervals).
		The function is a bijection from (a, b) to (c, d); being linear, it is continuos (since the inverse image of an open interval is an open interval), the inverse function is also linear and, hence, continuous.
	www-math.cudenver.edu /~puhalski/teaching/99-top/t1r/t1r.html (250 words)

	Matches for: Author=arhangelskii (Site not responding. Last check: 2007-11-07)
		Proceedings of the 15th Summer Conference on General Topology and its Applications/1st Turkish International Conference on Topology and its Applications (Oxford, OH/Istanbul, 2000).
		Proceedings of the 2000 Topology and Dynamics Conference (San Antonio, TX).
		Proceedings of the 13th Summer Conference on General Topology and its Applications (México City, 1998).
	www.math.unipd.it /~artico/reviews/arhangelskii.htm (1103 words)

	[No title]
		But as these truths prevail over the third millennium's first century or two, historians will have trouble (as did the author) finding a prior exposition of the emerging worldview that the text identifies and summarizes.
		Experience is any relatively unified and coherent interpretation of related contemporaneous sensations.
		The Earth is still spheroid and still moves around the Sun, even though the Sun is now known to not be the center of the universe.
	humanknowledge.net /HumanKnowledge.txt (17891 words)

	Structure of the Tetraspanin Main Extracellular Domain. A PARTIALLY CONSERVED FOLD WITH A STRUCTURALLY VARIABLE DOMAIN ...
		Topology of the Tetraspanin EC2-- From our data and the known structure of the CD81 EC2, it is possible to build general models for the topological organization
		relative to the conserved subdomain is conserved among tetraspanins.
		the residues of this region are relatively hydrophilic.
	www.jbc.org /cgi/content/full/276/43/40055 (5133 words)

	Re: relative topology in R^2
		First of all, what does the phrase 'relative topology' mean?
		What will be a base for the relative topologies on those sets?
		After considering that question, you may want to look at intersections of your sets A and B with elements of your original base.
	www.usenet.com /newsgroups/sci.math/msg23842.html (169 words)

	relative topology - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "relative topology" is defined.
		Relative Topology : Eric Weisstein's World of Mathematics [ home, info ]
		relative topology : PlanetMath Encyclopedia [ home, info ]
	www.onelook.com /?w=relative+topology (93 words)

	Publications of the research group from 1997 to December 2003
		M. Peikert, Examples of Weyl Geometries in Affine Differential Geometry, In: Geometry and Topology of Submanifolds Vol.
		Geometry and Topology of Submanifolds X, W.H. Chen et al.
		M. Wiehe, Remarks on Affine Variations on the Ellipsoid, In: Geometry and Topology of Submanifolds Vol.
	www.math.tu-berlin.de /geometrie/adg/dfg/dfg-publ.html (768 words)

	Human Anatomy [encyclopedia] (Site not responding. Last check: 2007-11-07)
		It originally referred to the cutting up of the body to determine the nature and organization of its parts, but nowadays it includes many other aspects of study.
		Topographic or gross anatomy deals with the relative positions of various body parts.
		Systemic anatomy is concerned with the study of groups of related structures (eg the respiratory system).
	kosmoi.com /Health/Medicine/Anatomy (958 words)

	AllRefer.com - topology (Mathematics) - Encyclopedia (Site not responding. Last check: 2007-11-07)
		You are here : AllRefer.com > Reference > Encyclopedia > Mathematics > topology
		topology, branch of mathematics, formerly known as analysis situs, that studies patterns of geometric figures involving position and relative position without regard to size.
		Topology is sometimes referred to popularly as "rubber-sheet geometry" because a figure can be changed to that of an equivalent figure by bending, stretching, twisting, and the like, but not by tearing or cutting.
	reference.allrefer.com /encyclopedia/T/topology.html (141 words)

	Science -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Because (A generalization of special relativity to include gravity (based on the principle of equivalence)) general relativity accounts for all of the phenomena that Newton's Laws do and more, general relativity is now regarded as a better theory.
		For example, Newtonian physics, and in more extreme cases relativity allow us to predict anything from the effect one moving billiard ball will have on another to things like trajectories of space shuttles and satellites.
		The social sciences allow us to predict (with limited accuracy for now) things like economic turbulence and also to better understand human behavior and to produce useful modles of society and to work more empirically with government policies.
	www.absoluteastronomy.com /Encyclopedia/s/sc/science.htm (4633 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		We observe that G has a nontrivial group topology, coarser than its natural topology, w.r.t.
		which it is amenable, viz the relative weak topology of C(X,M(n)).
		This topology seems more useful than other known amenable topologies for G. We construct a simple fermionic model containing an action of G, continuous w.r.t.
	www.ma.utexas.edu /mp_arc/a/04-14 (84 words)

	Atlas: A $\gamma$-set coincidence by Peter Nyikos (Site not responding. Last check: 2007-11-07)
		The speaker [2] and D. Ma [3] gave characterizations of \gamma-subsets of the real line which involved the compact-open topology on various spaces of continuous functions.
		Put the interval topology on X = T \cup A', so that T is a countable dense set of isolated points and X is locally compact.
		(U) consisting of those functions whose support is a finite subset of T, then R is Frechet-Urysohn in the relative topology iff A is a \gamma-set.
	atlas-conferences.com /cgi-bin/abstract/cakw-15 (300 words)

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