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Every closed subspace of a reflexive space is reflexive.
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Every and closed
Every time I closed my eyes, I saw Gray Eyes rushing at me with a knife.
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 unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.
Every character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.
* 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.
* Every closed subgroup of a profinite group is itself profinite ; the topology arising from the profiniteness agrees with the subspace topology.
Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G
* Every closed nowhere dense set is the boundary of an open set.
Every map that is injective, continuous and either open or closed is an embedding ; however there are also embeddings which are neither open nor closed.
Every base he closed resulted in a new construction project elsewhere to expand another base, relocation of forces projects and other related spending.
Every year the central business district ( with corners at the Municipal Building, Grand Street Fire House and Croton-Harmon High School ) is closed to automobile traffic for music, American food, local fund raisers, traveling, and local artists.
The generalized Poincaré conjecture states that Every simply connected, closed n-manifold is homeomorphic to the n-sphere.
Every closed 3-manifold has a prime decomposition: this means it is the connected sum of prime three-manifolds ( this decomposition is essentially unique except for a small problem in the case of non-orientable manifolds ).
: Every oriented prime closed 3-manifold can be cut along tori, so that the interior of each of the resulting manifolds has a geometric structure with finite volume.
* Every integrable subbundle of the tangent bundle — that is, one whose sections are closed under the Lie bracket — also defines a Lie algebroid.
* Every irreducible closed subset of P < sup > n </ sup >( k ) of codimension one is a hypersurface ; i. e., the zero set of some homogeneous polynomial.
Every October the high street is closed for the two Saturdays either side of 11 October for the Marlborough Mop Fair.
Every closed point of Hilb ( X ) corresponds to a closed subscheme of a fixed scheme X, and every closed subscheme is represented by such a point.
Every homeomorphism is open, closed, and continuous.
Every closed curve c on X is homologous to for some simple closed curves c < sub > i </ sub >, that is,
Every and subspace
* 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 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 subspace of a completely regular or Tychonoff space has the same property.
Every subgroup of a topological group is itself a topological group when given the subspace topology.
Every nontrivial proper rotation in 3 dimensions fixes a unique 1-dimensional linear subspace of R < sup > 3 </ sup > which is called the axis of rotation ( this is Euler's rotation theorem ).
* Every open subspace of a Baire space is a Baire space.
* Subspaces: Every subspace topology of the cofinite topology is also a cofinite topology.
* 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.
* Every closed subspace of X is spectral.
* Every subspace of a second-countable space is second-countable.
* Every direct summand of M is pure in M. Consequently, every subspace of a vector space over a field is pure.
Every vector space V with seminorm p ( v ) induces a normed space V / W, called the quotient space, where W is the subspace of V consisting of all vectors v in V with p ( v )
Every and reflexive
* Theorem Every reflexive normed space is a Banach space.
Every binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.
Every finite-dimensional normed space is reflexive, simply because in this case, the space, its dual and bidual all have the same linear dimension, hence the linear injection J from the definition is bijective, by the rank-nullity theorem.
Every finite-dimensional Hausdorff topological vector space is reflexive, because J is bijective by linear algebra, and because there is a unique Hausdorff vector space topology on a finite dimensional vector space.
Every semi-reflexive normed space is reflexive.
Every quotient of a reflexive space is reflexive.
* Every finite-dimensional reflexive algebra is hyper-reflexive.
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.
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 compact metric space is separable.
* 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.
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