** Every vector space has a basis.

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 vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.

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 finite-dimensional vector space is isomorphic to its dual space, but this isomorphism relies on an arbitrary choice of isomorphism ( for example, via choosing a basis and then taking the isomorphism sending this basis to the corresponding dual basis ).

Every random vector gives rise to a probability measure on R < sup > n </ sup > with the Borel algebra as the underlying sigma-algebra.

Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.

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 coalgebra, by ( vector space ) duality, gives rise to an algebra, but not in general the other way.

* Every holomorphic vector bundle on a projective variety is induced by a unique algebraic vector bundle.

For example, second-order arithmetic can express the principle " Every countable vector space has a basis " but it cannot express the principle " Every vector space has a basis ".

Many principles that imply the axiom of choice in their general form ( such as " Every vector space has a basis ") become provable in weak subsystems of second-order arithmetic when they are restricted.

Every vector space is free, and the free vector space on a set is a special case of a free module on a set.

** 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 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 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 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 dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

* Revised Code of Washington 9. 12. 010: " Every person who brings on his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of this state, with intent thereby to distress or harass a defendant in the suit, or who serves or sends any paper or document purporting to be or resembling a judicial process, that is not in fact a judicial process, is guilty of a misdemeanor ; and in case the person offending is an attorney, he or she may, in addition thereto be disbarred from practicing law within this state.

Disraeli wrote a personal letter to Gladstone, asking him to place the good of the party above personal animosity: " Every man performs his office, and there is a Power, greater than ourselves, that disposes of all this ..." In responding to Disraeli Gladstone denied that personal feelings played any role in his decision then and previously to accept office, while acknowledging that there were differences between him and Derby " broader than you may have supposed.

Every person should be identified uniquely as resident in one place but where they happen to be on census day, their de facto residence, may not be the best place to count them.

According to Every, one example may be " the myth of St. George " and other stories about saints battling dragons, which were " modelled no doubt in many cases on older representations of the creator and preserver of the world in combat with chaos ".

Cobham was a common butt of veiled satire in Elizabethan popular literature ; he figures in Ben Jonson's Every Man in His Humour and may have been part of the reason The Isle of Dogs was suppressed.

Every convict detained in a TBS-clinic may get temporary leave, after serving a certain time or after some progress in treatment.

Every key frame is numbered with a multi-digit identifier that may be referred to later.

Every RFC is submitted as plain ASCII text and is published in that form, but may also be available in other formats.

The last two lines of the Act IV-scene 2 funeral song may also have inspired the lines W. H. Auden, the librettist for Stravinsky's The Rake's Progress, puts into the mouth of Anne Truelove at the end of the opera: " Every wearied body must late or soon return to dust ".

Every compact Hausdorff space is also locally compact, and many examples of compact spaces may be found in the article compact space.

*: Articles 19 and 23 of the constitution provides, " Every person of I-Kiribati descent ... shall ... become or have and continue to have thereafter the right to become a citizen of Kiribati .... Every person of I-Kiribati descent who does not become a citizen of Kiribati on Independence Day ... shall, at any time thereafter, be entitled upon making application in such manner as may be prescribed to be registered as a citizen of Kiribati.

Every first Friday of the month, a trolley travels around Washington Street at different cafes and shops as artists showcase different pieces and may include auctions. This neighboorhod is scattered with urban blight ( within the residential section, from Caroll St east to the Brandywine Highway ).

Every point constructible using straightedge and compass may be constructed using compass alone.

Every non-inner automorphism yields a non-trivial element of Out ( G ), but different non-inner automorphisms may yield the same element of Out ( G ).

Every governing body is free to set its own standards, so the quality of races may differ.

Every gap sequence that contains 1 yields a correct sort ; however, the properties of thus obtained versions of Shellsort may be very different.

Every Dean of the Faculty ( equivalent to a Provost at most universities ) has always been an active-duty brigadier general, although technically, a civilian may hold the position.

The directive declared, " Every military commander has the responsibility to oppose discriminatory practices affecting his men and their dependents and to foster equal opportunity for them, not only in areas under his immediate control, but also in nearby communities where they may live or gather in off-duty hours.

From the Constitution of Lithuania, Article 32 ( 4 ): " Every Lithuanian person may settle in Lithuania.

Every kid is rated in running, batting, fielding, and pitching and has personality quirks that may affect the team.

Every late July ( ending on the last Saturday of July and beginning 10 days previous ) it hosts what may be the world's largest free-admission fair.

Every star of this type may usually be assigned a certain mean period.

Every 5 years the JNCC coordinates a compulsory review of schedules 5 and 8 to add new species that may need protection ( Legislation. gov. uk, 2010 ).