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Page "Preorder" ¶ 31
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Every and preorder
* Every finite topological space gives rise to a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder can be formed as the specialization preorder of a topological space in this way.
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 interior algebra can be represented as a preorder field with its interior and closure operators corresponding to those of the Alexandrov topology induced by the preorder.

Every and can
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.
** Well-ordering theorem: Every set can be well-ordered.
Every information exchange between living organisms — i. e. transmission of signals that involve a living sender and receiver can be considered a form of communication ; and even primitive creatures such as corals are competent to communicate.
Every context-sensitive grammar which does not generate the empty string can be transformed into an equivalent one in Kuroda normal form.
* Every regular language is context-free because it can be described by a context-free grammar.
Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form.
Every real number has a ( possibly infinite ) decimal representation ; i. e., it can be written as
Every module over a division ring has a basis ; linear maps between finite-dimensional modules over a division ring can be described by matrices, and the Gaussian elimination algorithm remains applicable.
Every entire function can be represented as a power series that converges uniformly on compact sets.
Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.
Every positive integer n > 1 can be represented in exactly one way as a product of prime powers:
Every sequence can, thus, be read in three reading frames, each of which will produce a different amino acid sequence ( in the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).
Every hyperbola is congruent to the origin-centered East-West opening hyperbola sharing its same eccentricity ε ( its shape, or degree of " spread "), and is also congruent to the origin-centered North-South opening hyperbola with identical eccentricity ε — that is, it can be rotated so that it opens in the desired direction and can be translated ( rigidly moved in the plane ) so that it is centered at the origin.
Every holomorphic function can be separated into its real and imaginary parts, and each of these is a solution of Laplace's equation on R < sup > 2 </ sup >.
Every species can be given a unique ( and, one hopes, stable ) name, as compared with common names that are often neither unique nor consistent from place to place and language to language.
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 morpheme can be classified as either free or bound.
Every use of modus tollens can be converted to a use of modus ponens and one use of transposition to the premise which is a material implication.
Every document window is an object with which the user can work.
Every adult, healthy, sane Muslim who has the financial and physical capacity to travel to Mecca and can make arrangements for the care of his / her dependants during the trip, must perform the Hajj once in a lifetime.
Every ordered field can be embedded into the surreal numbers.

Every and be
Every morning contingents of prisoners would be sent out to labor in nearby factories.
Every man who dabbles in the market to make a little easy money on the side and suffers losses could at the time hardly face his wife who was wondering how her husband could be so dumb.
Every policy officer cannot help but be a planning officer.
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.
Every Wednesday night through Oct. 11 there will be an elaborate colored fountain display, with 229 nozzles throwing jets of water up to 130 feet.
Every doll in the house must be going with her ''.
Every time a speech sound is produced for a given phoneme, it will be slightly different from other utterances, even for the same speaker.
Every previous experiment involving an anemometer had to be repeated.
* 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.
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 person holding the nationality of a Member State shall be a citizen of the Union.
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.
Every adult and wise woman without husband although reserves the right to accept concubinage for her employer / master without any coercion or force, but Islamic scholars have consensus that for sex relations options of Nikkah and Muta should be adopted instead of concubinage in this era.
" Every sign of unjust discrimination in their regard should be avoided.
George Every claims that the existence of " myths in the Bible would now be admitted by nearly everyone ", including " probably all Roman Catholics and a majority of Protestants ".
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 ".
Every compact metric space is complete, though complete spaces need not be compact.

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