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Every Hilbert space has this property.
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Every and Hilbert
Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.
* Every separable metric space is homeomorphic to a subset of the Hilbert cube.
Every subset of the Hilbert cube inherits from the Hilbert cube the properties of being both metrizable ( and therefore T4 ) and second countable.
It is more interesting that the converse also holds: Every second countable T4 space is homeomorphic to a subset of the Hilbert cube.
Every building has a canonical length metric inherited from the geometric realisation obtained by identifying the vertices with an orthonormal basis of a Hilbert space.
* Every Polish space is homeomorphic to a G < sub > δ </ sub > subspace of the Hilbert cube, and every G < sub > δ </ sub > subspace of the Hilbert cube is Polish.
( 5 ) Every continuous affine isometric action of G on a real Hilbert space has a fixed point ( property ( FH )).
Every commutative von Neumann algebra on a separable Hilbert space is isomorphic to L < sup >∞</ sup >( X ) for some standard measure space ( X, μ ) and conversely, for every standard measure space X, L < sup >∞</ sup >( X ) is a von Neumann algebra.
Every correspondence prescription between phase space and Hilbert space, however, induces its own proper-product.
* Every smooth Hilbert manifold can be smoothly embedded onto an open subset of the model Hilbert space.
* Every homotopy equivalence between two Hilbert manifolds is homotopic to a diffeomorphism.
Every and space
** Every vector space has a basis.
** Every infinite game in which is a Borel subset of Baire space is determined.
** Every Tychonoff space has a Stone – Čech compactification.
* Theorem Every reflexive normed space is a Banach space.
* Every topological space X is a dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification.
* Every compact metric space is separable.
* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.
* Pseudocompact: Every real-valued continuous function on the space is bounded.
Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.
Every compact metric space is complete, though complete spaces need not be compact.
Every point in three-dimensional Euclidean space is determined by three coordinates.
Every node on the Freenet network contributes storage space to hold files, and bandwidth that it uses to route requests from its peers.
Every space filling curve hits some points multiple times, and does not have a continuous inverse.
* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )
Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.
Every normed vector space V sits as a dense subspace inside a Banach space ; this Banach space is essentially uniquely defined by V and is called the completion of V.
Every and has
Every soldier in the army has, somewhere, relatives who are close to starvation.
Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every calculation has been made independently by two workers and checked by one of the editors.
Every retiring person has a different situation facing him.
Every family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
`` Every woman in the block has tried that ''.
: Every set has a choice function.
Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.
** Every surjective function has a right inverse.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
** Antichain principle: Every partially ordered set has a maximal antichain.
* Every small category has a skeleton.
* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
** Every field has an algebraic closure.
** Every field extension has a transcendence basis.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.
Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.
Every ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.
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