
	Where results make sense

Topic: Relatively compact subspace

Related Topics

Compact space

Normal family

Function space

Uniform convergence

Normal

Partition of a set

Mary Magdalene

In the News (Sun 27 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Compact Washer Dryers
		Maximal compact subgroup - In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups.
		Relatively compact subspace - In mathematics, a relatively compact subspace (or relatively compact subset) Y of a topological space X is a subset whose closure is compact.
		Compact star - In astronomy, a compact star (sometimes called a compact object) is a star that is a white dwarf, a neutron star, an exotic star, or a fl hole.
	wa72.theatredes2rives.com /compactwasherdryers.html (643 words)

	Relatively compact subspace - Wikipedia, the free encyclopedia
		In mathematics, a relatively compact subspace (or relatively compact subset) Y of a topological space X is a subset whose closure is compact.
		In the case of a metric topology, or more generally when sequences may be used to test for compactness, the criterion for relative compactness becomes that any sequence in Y has a subsequence convergent in X.
		Mahler's compactness theorem in the geometry of numbers characterises relatively compact subsets in certain non-compact homogeneous spaces (specifically spaces of lattices).
	en.wikipedia.org /wiki/Relatively_compact_subspace (215 words)

	Some Questions and References on Relative Topological Properties, Part 1
		Let Y be a (dense) subspace of a Tychonoff space X such that X is normal and countably paracompact (1-countably paracompact) on Y. Is then true that X x I is normal on Y x I? (Where I is the closed interval [0, 1]).
		Let Y be a (dense) subspace of a Tychonoff space X such that X x B is normal on Y x B, for each compact Hausdorff space B. Is then Y paracompact (1-paracompact) in X? Problem 17.
		Let Y be a (dense) subspace of a Tychonoff space X such that Y is internally normal in X and bounded in X. Is then Y countably compact in X? Problem 18.
	at.yorku.ca /i/a/a/i/04.htm (728 words)

	News \| Gainesville.com \| The Gainesville Sun \| Gainesville, Fla. (Site not responding. Last check: 2007-11-05)
		A compact subset of a Hausdorff space is closed.
		Every topological space X is a dense subspace of a compact space which has at most one point more than X.
		There are a number of topological properties which are equivalent to compactness in metric spaces, but are inequivalent in general topological spaces.
	www.gainesville.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=compact_space (1347 words)

	A.V. Arhangel'skii, I.V. Yaschenko
		Abstract:We consider the property of relative compactness of subspaces of Hausdorff spaces.
		Several examples of relatively compact spaces are given.
		We prove that the property of being a relatively compact subspace of a Hausdorff spaces is strictly stronger than being a regular space and strictly weaker than being a Tychonoff space.
	www.univie.ac.at /EMIS/journals/CMUC/cmuc9602/abs/yascenko.htm (51 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-11-05)
		The set-theoretic approach to the study of figures (spaces) is based on the study of the relative position of their elementary constituents.
		Each compact metric space is complete, but the converse is false; the simplest example is an infinite discrete space with the trivial metric.
		Cohen's construction of relative injective envelopes in the category of real Banach spaces [a3], the Aronszain–Panitchpakdi theorem that an injective real Banach algebra is an injective metric space [a1], and the Mazur–Ulam theorem that every isometry of real Banach spaces is affine [a9].
	eom.springer.de /m/m063680.htm (3081 words)

	[No title]
		This assumption together with a suitable compactness property of $g$ guarantees that $N$ is condensing with respect to a specific measure of non-compactness in the space of continuous functions on $[0,T]$.
		Now we consider a compact, convex subset $C$ of $E$ and a countable set $M\subset L^{2}(I;C) $, We claim that $S_{n}(M)(t) $ is relatively compact in $E$ for every $t\in I$.
		By Hausdorff's Theorem, $S(M) $ is relatively compact in $C(I;E) $.
	www.maths.tcd.ie /EMIS/journals/EJDE/Volumes/Monographs/Monographs/Volumes/2002/04/couchouron-tex (4279 words)

	News \| Gainesville.com \| The Gainesville Sun \| Gainesville, Fla. (Site not responding. Last check: 2007-11-05)
		One of the most remarkable facts about a locally compact group G is that it carries an essentially unique natural measure, the Haar measure, which allows one to consistently measure the "size" of sufficiently regular subsets of G.
		The group operation on the dual group is given by pointwise multiplication of characters, the inverse of a character is its complex conjugate and the topology on the space of characters is that of uniform convergence on compact sets (i.e., the compact-open topology).
		The dual group of a locally compact abelian group is introduced as the underlying space for an abstract version of the Fourier transform.
	www.gainesville.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Pontryagin_duality (1939 words)

	FuncAna
		Compact and relatively compact sets in metric spaces.
		Local weak compactness of the dual spaces of normed vector spaces: closed bounded sets in the dual space are weakly compact.
		Local weak compactness of reflexive Banach spaces: closed bounded sets in a reflexive Banach space are weakly compact.
	www.math.ttu.edu /~vshubov/FuncAna/FuncAna.html (947 words)

	hyperspace
		Two compact subsets A and B of S are close to each other provided that every point in each of the subsets is close to some point in the other subset.
		There are three which have their own symbols: H(S) denotes the hyperspace of all compact subsets of S; C(S) denotes the hyperspace of all connected compact subsets of S, and Fn(S) denotes the hyperspace of all subsets of S containing exactly n points.
		We start with a compact metric space M and consider the collection H(M) consisting of all the subsets of M which are compact.
	www.spsu.edu /math/stricklen/Hyperspace/hyperspace.htm (1827 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-11-05)
		, is (relatively) compact in the topology of uniform convergence on
		The proof of the main statements in the theory of almost-periodic functions is based on the consideration of integral equations on a group (cf.
		Invariant integration on an abstract compact group has been constructed [4] depending on an extension of the Peter–Weyl theory to this case.
	eom.springer.de /a/a011980.htm (745 words)

	locally_compact (Site not responding. Last check: 2007-11-05)
		All open or closed subsets of a locally compact Hausdorff space are locally compact in the subspace topology.
		Every locally compact Hausdorff space is a Baire space.That is, the conclusion of the Baire category theorem holds: the interior of every union of countably many nowhere dense subsets is empty.
		The notion of local compactness is important in the study of topological groups mainly because every locally compact Hausdorff group G carries natural measures called the Haar measures which allow one to integrate functions defined on G.
	www.900freedietplans.com /wiki/?title=Locally_compact (846 words)

	Compact operator - Wikipedia, the free encyclopedia
		In functional analysis, a branch of mathematics, a compact operator (or completely continuous operator) is a linear operator L from a Banach space X to another Banach space Y, such that the image under L of any bounded subset of X is a relatively compact subset of Y.
		The origin of the theory of compact operators is in the theory of integral equations.
		The compact operators from a Banach space to itself form a two-sided ideal in the algebra of all bounded operators on the space.
	en.wikipedia.org /wiki/Compact_operator (645 words)

	Springer Online Reference Works (Site not responding. Last check: 2007-11-05)
		Weyl, 1909) on the invariance of the condensation spectrum (the complement in the spectrum of the set of isolated eigenvalues of finite multiplicity) of a self-adjoint operator under compact perturbations.
		-image into a compact set), which implies that the essential spectra of the self-adjoint extensions of a wide class of symmetric multi-dimensional differential operators coincide.
		The Weyl–von Neumann theorem shows that the essential spectrum is the unique spectral characteristic of self-adjoint operators which is stable under compact perturbations, and that the continuous and point spectra are extremely unstable.
	eom.springer.de /s/s086330.htm (1219 words)

	Compact space - Wikipedia, the free encyclopedia
		For example, in R, the closed unit interval [0, 1] is compact, but the set of integers Z is not (it is not bounded) and neither is the half-open interval [0, 1) (it is not closed).
		The spectrum of any continuous linear operator on a Hilbert space is a compact subset of C.
		If the metric space X is compact and an open cover of X is given, then there exists a number δ > 0 such that every subset of X of diameter < δ is contained in some member of the cover.
	en.wikipedia.org /wiki/Compact_space (1390 words)

	Compact Operator -- from Wolfram MathWorld
		The basic example of a compact operator is an infinite diagonal matrix
		It is a compact operator because it is the limit of the finite rank matrices
		The properties of compact operators are similar to those of finite-dimensional linear transformations.
	mathworld.wolfram.com /CompactOperator.html (163 words)

	[No title]
		Namely we prove that every monotone operator on a subspace of a Banach space containing densely a continuous image of an Asplund space (these spaces are called GSG spaces) is singlevalued on the whole space except a $\sigma $-cone supported set.
		Abstract:The extension theorem of bounded, weakly compact, convex set valued and weakly countably additive measures is established through a discussion of convexity, compactness and existence of selection of the set valued measures; meanwhile, a characterization is obtained for continuous, weakly compact and convex set valued measures which can be represented by Pettis-Aumann-type integral.
		We find the compactness of the incompressible part $u$ of the velocity field $v$ and we give a new proof of the compactness of the ``effective pressure'' ${\Cal P} = \rho ^\gamma - (2\mu _1 +\mu _2) div v$.
	www.math.helsinki.fi /EMIS/journals/CMUC/cmuc9602/abstrall.htm (1300 words)

	Array convergence of functions of the first Baire-class
		of elements in a pointwise compact subset of the Baire-1 functions on a Polish space, whose iterated pointwise limit
		In angelic spaces the notions of (relative) compactness, (relative) countable compactness and (relative) sequential compactness coincide.
		A device of R. Whitley's applied to pointwise compactness in spaces of continuous functions, Proc.
	www.math.utep.edu /Faculty/helmut/baire/baire.html (753 words)

	The Klein-Millman Theorem
		We use Zorn's Lemma to find a maximal relatively open convex proper subset and then show its complement is a singleton.
		be the relatively open convex proper subsets, ordered by inclusion.
		is an open cover of compact sets, and so there is a finite subcover.
	www.math.unl.edu /~s-bbockel1/929/node17.html (262 words)

	Subspace
		* In mathematics, if a set with certain properties is called a space, then a subset with the same properties is usually called a subspace.
		Of a metric space, or topological subspace in topology, any subset can be taken; however, a linear subspace (also called vector subspace) in linear algebra is a special subset.
		5ub5p4c3 aubspace dubspace eubspace sbspace sbuspace shbspace sibspace sjbspace ssubspace subapace subbspace subdpace subepace subpace subpsace subsace subsapce subslace subsoace subsp4c3 subspaace subspac subspacce subspace subspacee subspade subspae subspaec subspafe subspave subspaxe subspcae subspce subsppace subspqce subspsce subspwce subspzce subsspace subwpace subxpace subzpace sugspace suhspace sunspace susbpace suspace suubspace suvspace sybspace usbspace wubspace xubspace zubspace
	www.mispedia.org /Subspace.html (109 words)

	Diary for Math 507:01, spring 2004
		Also, If M is a subspace of V, and v is in V, then there is a continuous linear functional which is 0 on M and is d on v, where d is infv+m
		A map in L(H) is compact iff it is the limit of maps with finite dimensional range.
		I showed that this kernel was a reproducing kernel, and that the series defining it in terms of an orthonormal basis converged uniformly on compact sets, was both holomorphic in one variable and anti-holomorphic in the other, and didn't depend on choice of basis.
	www.math.rutgers.edu /~greenfie/mill_courses/math507/diary.html (4537 words)

	Topological property - Wikipedia, the free encyclopedia
		Every subspace of a compact space (including the compact space itself) is relatively compact.
		This is, strictly speaking, not a topological invariant of the space, but depends on how it is embedded as a subspace.
		A space is Boolean if it is zero-dimensional, compact and Hausdorff (equivalently, totally disconnected, compact and Hausdorff).
	en.wikipedia.org /wiki/Topological_property (1281 words)

	HJM, Vol. 25, No. 4, 1999
		It is shown that the span of the boundary of C is a lower bound for both the span and semispan of X.
		It is also shown that if a span of X is equal to the breadth of X and Y satisfies certain conditions relative to X then thatspan of X is an upper bound for the corresponding span of Y.
		As application, we show that if G is a compact metrizable abelian group and Lambda is a Riesz subset of its dual then every countably additive A-valued measure with bounded variation and whose Fourier transform is supported by Lambda has relatively* compact range.
	www.math.uh.edu /~hjm/Vol25-4.html (1355 words)

	Bases and basic sequences (Site not responding. Last check: 2007-11-05)
		An F-space E is said to be pseudo-Fr echet if the weak topology on each linear subspace coincides on bounded sets with the weak topology of the whole space.
		An F-space E is said to be pseudo-reflexive if the weak topology is Hausdorff and if every bounded set is relatively compact in the weak topology of its closed linear span.
		We give criteria for an F-space to be pseudo-Fr echet or pseudo-reflexive in terms of shrinking and boundedly complete basic sequences.
	www.mth.msu.edu /~shapiro/Pubvit/Downloads/BasesBasic/BasesBasic.html (118 words)

	Compact Convector Heater (Site not responding. Last check: 2007-11-05)
		Dimplex Compact Electric Stove Heater Dimensions: 20.3" W x 13" D x 23.5
		Inquirer Compact - The Inquirer Compact is one of two trimmed-down versions of the Philippine Daily Inquirer, the other being the Inquirer Libre.
		The Inquirer Compact, unlike the Inquirer broadsheet, is printed in the compact format, and unlike the Inquirer Libre, is not free of charge.
	po59.georgeandbills.com /compactconvectorheater.html (709 words)

	Compact Washer Dryers (Site not responding. Last check: 2007-11-05)
		It should be freestanding for proper air circulation.
		Coxreels Compact Air Water Hose Reel Prices - Pressure Washers Coxreels Compact Air Water Hose Reel Prices Best Prices on Pressure Washers "Compact, lightweight hand crank hose reel holds 150 feet f...
		Slik Compact-XL Compact Travel Tripod Prices - Slik Slik Compact-XL Compact Travel Tripod Prices Best Prices on Slik Slik Compact-XL Compact Travel Tripod CLICK FOR BEST PRICE/DETAILS Slik - Great...
	ma77.georgeandbills.com /compactwasherdryers.html (1069 words)

	General Topology: Elements of Mathematics, Chapters 1-4:3540642412:Bourbaki, Nicolas:eCampus.com
		Image of a compact space under a continuous mapping
		Embedding of a locally compact space in a compact space
		Groups operating properly on a topological space; compactness in topological groups and spaces with operators
	www.ecampus.com /bk_detail.asp?isbn=3540642412 (357 words)

Try your search on: Qwika (all wikis)