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Topic: Locally convex

Related Topics

convex hull

convex function

Locally convex topological vector space

Convex Computer

locally convex

convex lens

Proper convex function

Minimal convex decomposition

convex set

convex polytope

Plano convex

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	PlanetMath: locally convex topological vector space
		is a locally convex topological vector space [1].
		"locally convex topological vector space" is owned by mathcam.
		This is version 6 of locally convex topological vector space, born on 2003-07-05, modified 2006-02-17.
	planetmath.org /encyclopedia/LocallyConvexTopologicalVectorSpace.html (134 words)

	Convex
		For example, a solid cube is convex, but anything that is hollow or has a dent in it is not convex.
		The intersection of any collection of convex sets is itself convex, so the convex subsets of a (real or complex) vector space form a complete lattice.
		A convex function defined on some interval is continuous on the whole interval and differentiable at all but at most countably many points.
	www.ebroadcast.com.au /lookup/encyclopedia/co/Convex.html (427 words)

	Springer Online Reference Works
		A central topic in the theory of locally convex spaces (and also in the theory of topological vector spaces) is the study of the relation of the space with its dual or adjoint space.
		A notable role in the theory of locally convex spaces is played by methods of homological algebra connected with the study of the category of locally convex spaces and their continuous mappings, and also some subcategories of this category.
		Locally convex spaces arise in great profusion throughout such fields of analysis as measure and integration theory, complex analysis in one, several or an infinite number of variables, partial differential equations, integral equations, approximation theory, operator and spectral theory, as well as probability theory.
	eom.springer.de /L/l060360.htm (1540 words)

	Topological vector space - Wikipedia, the free encyclopedia
		Local convexity is the minimum requirement for "geometrical" arguments like the Hahn-Banach theorem.
		Bornological space: a locally convex space where the continuous linear operators to any locally convex space are exactly the bounded linear operators.
		Fréchet spaces: these are complete locally convex spaces where the topology comes from a translation-invariant metric, or equivalently: from a countable family of semi-norms.
	en.wikipedia.org /wiki/Topological_vector_space (1125 words)

	PlanetMath: Krein-Milman theorem
		is the closed convex hull of its extreme points.
		The closed convex hull above is defined as the intersection of all closed convex subsets of
		This turns out to be the same as the closure of the convex hull in a topological vector space.
	planetmath.org /encyclopedia/KreinMilmanTheorem.html (132 words)

	Springer Online Reference Works
		In particular, the least upper bound of a family of locally convex topologies on a given vector space, the induced topology on a subspace and the topology of a product of locally convex topologies are projective topologies (and therefore locally convex topologies).
		In particular, the quotient topology of a given locally convex topology and the topology of a direct sum of locally convex topologies are inductive topologies (and therefore locally convex topologies).
		The concepts of projective and inductive locally convex topologies make it possible to define the operations of projective and inductive limits in the category of locally convex spaces and their linear mappings.
	eom.springer.de /l/l060370.htm (310 words)

	Locally convex topological vector space - Wikipedia, the free encyclopedia
		Although in general such spaces are not necessarily normable, the existence of a convex local base for the zero vector is strong enough for the Hahn-Banach theorem to hold, yielding a sufficiently rich theory of continuous linear functionals.
		In particular it is not locally convex, and its dual space is 0.
		Because locally convex spaces are topological spaces as well as vector spaces, the natural functions to consider between two locally convex spaces are continuous linear maps.
	en.wikipedia.org /wiki/Locally_convex_topological_vector_space (2109 words)

	Springer Online Reference Works
		General questions in the theory of locally convex lattices are the following: The study of the connections between topological properties and order properties; in particular, the topological properties of bands and positive cones in a locally convex lattice and connections between lattice properties and topological properties of completeness in a locally convex lattice.
		The study of properties of the strong dual of a locally convex lattice and properties of the imbedding of a locally convex lattice
		The most important example of a locally convex lattice is a Banach lattice.
	eom.springer.de /l/l060350.htm (182 words)

	Springer Online Reference Works
		The Mackey topology is the strongest of the separated locally convex topologies (cf.
		Locally convex topology) which are compatible with the duality between
		Completions, quotient spaces and metrizable subspaces, products, locally convex direct sums, and inductive limits of families of Mackey spaces are Mackey spaces.
	eom.springer.de /m/m062080.htm (199 words)

	$Q$-reflexive locally convex spaces, Christopher Boyd, Seán Dineen, Milena Venkova
		For a locally convex space $E$ we use the Aron-Berner extension to define canonical mappings from $\pin E_e''$ into different duals of $\sP(^nE)$.
		Boyd, C., Duality and reflexivity of spaces of approximable polynomials on locally convex spaces, Monatsh.
		Defant, A., The local Radon Nikodým property for duals of locally convex spaces, Bulletin de la Société Royale des Sciencies de Liège, 53e année, 5 (1984), 233-246.
	projecteuclid.org /getRecord?id=euclid.prims/1145475965 (344 words)

	Annotated Bibliography on the Range of Vector Measures (Site not responding. Last check: 2007-10-11)
		Bazhenov (1986) gave a complete characterization of locally convex spaces to which he extended the theorem of Lyapunov.
		Goller (1984) extended the convexity theorem of Lyapunov considering weak^*-continuous linear mappings of the dual space of a normed vector lattice into a topological Hausdorff space.
		Kühn and Rösler (1998) showed that although convexity and compactness conclusions of Lyapunov's theorem may fail for measures defined on different sigma-algebras of the same set, they do hold if the sigma-algebras are nested, which is exactly the setting of classical optimal stopping theory.
	www.math.gatech.edu /~hill/publications/annotated.html (5995 words)

	Determining Convexity of Polyhedra
		A 3D simplicial polyhedron G is the surface of a convex polytope if and only if G is locally convex, and the projection of the seam of G is a globally convex polygon.
		In addition, the z-projection of the seam of a convex polyhedron will also be convex, and so will the projection of the seam of G. See the diagram in the definitions for a better idea of why this might be so.
		Going the other way is a little bit more difficult, where we're trying to show that a polyhedron G which is locally convex, with a seam z-projection which is itself a convex polygon, is the surface bounding a convex polytope (a convex polyhedron).
	www.cs.mcgill.ca /~tflook/geo/algorithm.html (1268 words)

	[No title]
		A topological vector space is "locally convex" if the origin has a basis of neighborhoods that are convex.
		The dual V* of a locally convex topological vector space V naturally becomes a locally convex topological vector space with the so-called "weak topology".
		By this means the space of distributions and the space of hyperfunctions on the circle become locally convex topological vector spaces.
	www.math.niu.edu /~rusin/known-math/98/TVS (906 words)

	Augmented Uniform Polyhedra
		(Care must be taken in the selection of the excavating polyhedron, it must itself be locally convex, it must have the requisite pyramidical symmetry (3-, 4- or 5-fold) and it must be sized such that the new vertices are visible on the exterior of the resulting polyhedron.) I term the convexity of these polyhedra 'potential'.
		The excavation must be deep enough to re-create a (highly wound) locally convex vertex (with opposite polarity to the original).
		The remaining excavations are deep enough to re-create a (highly wound) locally convex vertex (with opposite polarity to the original).
	web.ukonline.co.uk /polyhedra/uniform/augmented/augment.html (1294 words)

	Atlas: On locally quasi-convex groups by Elena Martin-Peinador (Site not responding. Last check: 2007-10-11)
		Locally quasi-convex groups were introduced by Vilenkin [5] in the 50's.
		It is proved there that the class of locally quasi-convex groups contains the class of locally convex vector spaces.
		Thus, locally quasi-convex groups are the natural generalization of the latter.
	atlas-conferences.com /cgi-bin/abstract/caey-71 (364 words)

	Completeness Properties of Locally Quasi-Convex Groups. (ResearchIndex)
		Abstract: It is natural to extend the Grothendieck Theorem on completeness, valid for locally convex topological vector spaces, to abelian topological groups.
		The adequate framework to do it seems to be the class of locally quasi-convex groups.
		By means of the continuous convergence structure on the dual of a topological group, we also state some weaker...
	citeseer.ist.psu.edu /429470.html (470 words)

	Locally convex approach spaces by M. Sioen and S. Verwulgen (Site not responding. Last check: 2007-10-11)
		We continue the investigation of suitable structures for quantified functional analysis, by looking at the notion of local convexity in the setting of approach vector spaces as introduced in [Approach vector spaces].
		We prove that the locally convex objects are exactly the ones generated (in the usual approach sense) by collections of seminorms.
		Furthermore, we construct a quantified version of the projective tensor product and show that the locally convex objects admitting a decent exponential law with respect to it are precisely the seminormed spaces.
	at.yorku.ca /i/a/a/j/76.htm (145 words)

	University of North Dakota in Grand Forks, North Dakota
		One is functional analysis, specifically locally convex spaces and distributions.
		In his endeavor, Schwartz carefully studied locally convex spaces and this area of mathematics continues to be active today.
		Such a space is obtained by taking unions of increasing sequences of locally convex spaces, then putting a linear structure on the union (a locally convex topology) in order to study properties like completeness or bounded sets.
	www.und.nodak.edu /instruct/gilsdorf/webpages/research.html (279 words)

	AMCA: An Elementary Approach to Locally Convex Operator Spaces by Susanne Dierolf (Site not responding. Last check: 2007-10-11)
		The aim of this talk is to present an introduction to the theory of locally convex operator spaces which is completely elementary and utilizes only the standard tools of usual locally convex spaces - an introduction "from below".
		It turns out that locally convex operator spaces can be treated very similarly to usual locally convex spaces and that most of the topics for locally convex spaces have an analogue in the category of locally convex operator spaces.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/f/v/98.htm (169 words)

	Locally Convex (Concave) Games (ResearchIndex)
		If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
		Therefore locally convex games can be considered as relaxations of convex games.
		Moreover, we obtain a characterization of a subclass of locally concave games in terms of the rank function of a matroid.
	citeseer.ist.psu.edu /453218.html (288 words)

	Hahn-Banach Separation Theorems
		Answer: Convex sets almost always can be separated under mild topological conditions.
		a nonempty, convex balanced set, which is absorbing at each point, the function
		is convex (this is where we use the fact
	www.math.unl.edu /~s-bbockel1/929/node2.html (184 words)

	The H∞-optimization in locally convex spaces
		-control theory is extended to locally convex spaces through the form of a parameter.
		The algorithms of computing the infimal model-matching error and the infimal controller are presented in a locally convex space.
		Two examples with the form of a parameter are enumerated for computing the infimal model-matching error and the infimal controller.
	www.hindawi.com /GetArticle.aspx?doi=10.1155/S1048953302000102 (100 words)

	Amazon.com: Foundations of Complex Analysis in Non Locally Convex Spaces: Function Theory without Convexity Condition ... (Site not responding. Last check: 2007-10-11)
		However, the theory without convexity condition is covered for the first time in this book.
		Foundations of Complex Analysis in Non Locally Convex Spaces is a comprehensive book that covers the fundamental theorems in Complex and Functional Analysis and presents much new material.
		The new concept of Quasi-differentiability introduced by the author represents the backbone of the theory of Holomorphy for non-locally convex spaces.
	amazon.com /Foundations-Complex-Analysis-Locally-Convex/dp/0444500561 (966 words)

	Dilations on locally convex spaces., James E. Simpson
		Dilations on locally convex spaces., James E. Simpson
		[6] H. Schaefer, Spectral measures in locally convex algebras, Acta Math., 107 (1962), 125-173.
		[10] B. Walsh, Structure of spectral measures on locally convex spaces, Trans.
	projecteuclid.org /getRecord?id=euclid.pjm/1102724970 (152 words)

	Schottenloher: The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder ...
		The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition.
		It is proved that the Levi problem for certain locally convex Hausdorff spaces
		It is also shown that a pseudoconvex domain spread over a Fréchet space or a Silva space with a finite dimensional Schauder decomposition is holomorphically convex and satisfies an approximation theorem of the Oka-Weil type.
	www.numdam.org /numdam-bin/item?id=AIF_1976__26_4_207_0 (494 words)

	The Orbit of the Moon around the Sun is Convex! (Site not responding. Last check: 2007-10-11)
		It is locally convex in the sense that it has no loops and the curvature never changes sign.
		Since the eccentricities are small, we can assume that the orbits of the Earth around the Sun and the Moon around the Earth are both circles.
		“The Sun, the Moon, and Convexity” by Noah Samuel Brannen in The College Mathematics Journal v.
	www.math.nus.edu.sg /aslaksen/teaching/convex.html (606 words)

	DC MetaData for: Phelps' Lemma, Danes' Drop Theorem and Ekeland's Principle in Locally Convex Topological Vector Spaces (Site not responding. Last check: 2007-10-11)
		Abstract: We present a generalization of the Phelps lemma to locally convex topological vector spaces and show the equivalence of this theorem, Ekeland's principle and Danes' drop theorem in locally convex spaces to their Banach space counterparts and to a Pareto efficieny theorem due to Isac.
		We show that another formulation of Ekeland's principle in locally convex spaces using a family of topology generating semi-norms as perturbation functions rather than a single (in general discontinuous) Minkowski functional turns out to be equivalent to the original version.
		The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.
	www.mathematik.uni-halle.de /reports/shadows/01-10report.html (169 words)

	The Locally Convex Topology on the Space of Meromorphic Functions (Site not responding. Last check: 2007-10-11)
		A Theorem of his that is related to the Mittag-Leffler theorem looks like a duality result under some locally convex topology on the space of meromorphic functions.
		The main tool in the study of this topology is a projective description of it that is derived here.
		We also argue that Holdgrun's topology is the natural locally convex topology on the space of meromorphic functions.
	anziamj.austms.org.au /JAMSA/V59/part3/Grosse.html (154 words)

	Kalton: The three space problem for locally bounded $F$-spaces
		Kalton, N. The three space problem for locally bounded $F$-spaces.
		: A convexity condition in Banach spaces and the strong law of large numbers.
		: On a convexity condition in normed linear spaces.
	math-doc.ujf-grenoble.fr /numdam-bin/item?id=CM_1978__37_3_243_0 (112 words)

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