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Topic: Pseudometric

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	Baire category theorem - Wikipedia, the free encyclopedia
		More generally, every topological space which is homeomorphic to an open subset of a complete pseudometric space is a Baire space.
		Relation to AC The proofs of BCT1 and BCT2 require some form of the axiom of choice; and in fact the statement that every complete pseudometric space is a Baire space is logically equivalent to a weaker version of the axiom of choice called the axiom of dependent choice.
		BCT1 is used to prove the open mapping theorem, the closed graph theorem and the uniform boundedness principle.
	en.wikipedia.org /wiki/Baire_category_theorem (378 words)

	Humboldt State University: Math Department (Site not responding. Last check: 2007-08-08)
		In 1903, Hilbert introduced a projective pseudometric on positive vectors for the purpose of further studying the geometry of Lobatschefsky and Bolyai.
		In 1957, Garrett Birkhoff resurrected the metric, showed that a positive square matrix operating on the set of positive vectors of the same size is a contraction mapping with respect to it, and derived Perron’s Theorem as a corollary.
		Hilbert’s pseudometric is not familiar to many mathematicians, but is used a lot by economists, who are responsible for some of these extensions.
	www.humboldt.edu /~math/currentevents/colloquim/archives/fall_03/nov06-03.htm (527 words)

	PlanetMath: pseudometric topology
		whose pseudometric topology coincides with the given topology for
		Cross-references: symmetric, triangle inequality, cover, pseudometric, induced, topology, base, collection, metric space, pseudometric space
		This is version 3 of pseudometric topology, born on 2004-10-03, modified 2004-10-27.
	planetmath.org /encyclopedia/PseudometricTopology.html (133 words)

	[No title]
		I was unfortunately unable to bring up the plot of the horizons on the pseudometric.
		The -> embedding of the equatorial plane is certainly a bag of gold, -> but the embedding of the rho-z plane is probably not.
		I'll try to detail my physical intuition on this point, and see if it matches with the way you are thinking about things.
	wugrav.wustl.edu /research/projects/old_cocoboard/3DWAVES/00260 (883 words)

	A Further Investigation for Fuzzy Measures on Metric Spaces (ResearchIndex) (Site not responding. Last check: 2007-08-08)
		Abstract: The pseudometric generating property of non-additive set functions also plays an important role as the autocontinuity in fuzzy measure theory [2, 9].
		The aim of this paper is to prove the Egoroff's theorem and Lusin's theorem for measurable functions on metric spaces hold for those fuzzy measures with the exhaustivity and pseudometric generating property.
		1 Pseudometric generating property and autocontinuity of fuzzy..
	citeseer.ist.psu.edu /51956.html (310 words)

	PlanetMath: pseudometric space
		In other words, a pseudometric space is a generalization of a metric space in which we allow the possibility that
		See Also: metric space, quasimetric space, normed vector space, seminorm
		This is version 4 of pseudometric space, born on 2004-10-02, modified 2004-10-07.
	planetmath.org /encyclopedia/Pseudometric.html (74 words)

	[No title] (Site not responding. Last check: 2007-08-08)
		I am sure that youn are correct about the lengths of the pseudometric being the areas of the surfaces, so yes, the inner horizon should be a maximum of the pseudometric.
		I don't think that the problem is one of boundaries, but rather one of competing effects.
		Now, the length of the curve is the line integral of the pseudometric.
	wugrav.wustl.edu /research/projects/old_cocoboard/3DWAVES/00300 (600 words)

	Mathematical ASCII Notation - Mathematics - Apronus.com
		Despite its limitations the Math ASCII Notation has much expressive power, as can be seen from browsing through these pages.
		Let Y be an outer measure on X. Define the corresponding pseudometric on P(X).
		Let Y be an outer measure on X, and let d be the corresponding pseudometric on P(X).
	www.apronus.com /math/mathascii99/mathascii60.htm (548 words)

	Sampling-based methods
		The time-dependency of obstacle models must be taken into account when verifying that path segments are collision free; the techniques from Section 6.3.4 can be extended to handle this.
		For some algorithms, it may be important to permit the use of a pseudometric because symmetry is broken by time (going backward in time is not as easy as going forward).
		The metric can be extended across time to obtain a pseudometric,
	msl.cs.uiuc.edu /planning/node326.html (220 words)

	AIF : Tome 54 fascicle 3 -- 2004
		This article gives a description, by means of functorial intrinsic fibrations, of the geometric structure (and conjecturally also of the Kobayashi pseudometric, as well as of the arithmetic in the projective case) of compact Kähler manifolds.
		We first define special manifolds as being the compact Kähler manifolds with no meromorphic map onto an orbifold of general type, the orbifold structure on the base being given by the divisor of multiple fibres.
		also gives a very simple conjectural qualitative of description of both the Kobayashi pseudometric and the distribution of its
	annalif.ujf-grenoble.fr /Vol54/E543_1/E543_1.html (291 words)

	[No title]
		The disk on the left is "inflated" on the right, by a pseudometric function of the boundary.
		A signed implicitization, and a sweep of its level sets.
		If the shapes are "implicitized" as signed pseudometric functions of the surface boundaries, shapes will grow or shrink continuously as the boundaries reconform to their targets.
	www-graphics.stanford.edu /workshops/ibr98/Talks/Lance/silhouettes.html (525 words)

	DBLP: Franck van Breugel
		Franck van Breugel, Claudio Hermida, Michael Makkai, James Worrell: An Accessible Approach to Behavioural Pseudometrics.
		Franck van Breugel, James Worrell: A behavioural pseudometric for probabilistic transition systems.
		Franck van Breugel, Michael W. Mislove, Joël Ouaknine, James Worrell: Domain theory, testing and simulation for labelled Markov processes.
	sunsite.informatik.rwth-aachen.de /dblp/db/indices/a-tree/b/Breugel:Franck_van.html (290 words)

	On a class of hereditarily paracompact spaces by Heikki Junnila, Hans-Peter A. Kunzi and Stephen Watson (Site not responding. Last check: 2007-08-08)
		\tau there is a pseudometric p on X such that \tau
		The property of upholsteredness is preserved under closed continuous surjections.
		Keywords: Upholstered, perfect, paracompact, quasi-pseudometric, pseudometric, semi-stratifiable, transitive space
	at.yorku.ca /b/a/a/k/76.htm (119 words)

	Ingarden proof (Site not responding. Last check: 2007-08-08)
		converging on B, and any sequence converging to A contains a subsequence convergent to a subring of A. If a Boolean ladder admits a real-valued function F, it is a pseudometric space with a pseudometric distance defined in a more or less obvious way that I won't present here.
		A pseudometric is a non-negative symmetric function of A and B which disappears for A = B, but not necessarily only then.
		Information can be defined in two equivalent ways, one simpler, but using expressions N
	www.nu.ac.za /undphil/collier/information/ingarden.html (520 words)

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