** Every field has an algebraic closure.

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 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 field has an algebraic closure, and it is unique up to an isomorphism that fixes F.

This flat may be identified with the partition of the vertices of into the connected components of the subgraph formed by: Every set of edges having the same closure as gives rise to the same partition of the vertices, and may be recovered from the partition of the vertices, as it consists of the edges whose endpoints both belong to the same set in the partition.

* Let K < sup > a </ sup > be an algebraic closure of K containing L. Every embedding σ of L in K < sup > a </ sup > which restricts to the identity on K, satisfies σ ( L ) = L. In other words, σ is an automorphism of L over K.

Every interior algebra can be represented as a topological field of sets with its interior and closure operators corresponding to those of the topological space.

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 physical quantity has a Hermitian linear operator associated to it, and the states where the value of this physical quantity is definite are the eigenstates of this linear operator.

Every spin network is an eigenstate of each such operator, and the area eigenvalue equals

Every generalized eigenvalue of a normal operator is thus genuine.

Every operator also received 80 hours of medical training.

Every delta operator ' has a unique sequence of " basic polynomials ", a polynomial sequence defined by three conditions:

Every motion of the lock is derived from movement of the hands rather than elements beyond the operator ’ s control, such as dirt, rust, or memory.

* Every first time purchaser of an automobile deprived the streetcars operator of income whilst simultaneously created additional traffic congestion which often reduced service speeds and thereby increased their operational costs and making the services less attractive to the remaining users.

Is fundamental for the many-body theory that Every operator can be expressed in terms of annihilation and creation operators.

Every operator can then route calls directly to their own customers, or pass them on to another operator if the call is not for one of their customers.

Every self-adjoint operator is normal.

Every symmetric operator is closable.

Every self-adjoint operator is maximal symmetric.

Every self-adjoint operator is densely defined, closed and symmetric.

Every operator in the unit is cross-trained in a variety of " low-visibility " skills such as weapons, survival, sniping, medic, small boat handling, driving, tracking, air ops etc.

where the rank refers to the rank of the linear operator F. Every nonsimple bivector can be written as a sum of at most two simple ones.

Every day, when the President took his nap, Rob Roy would stretch out on the window seat near him, like a perfect gentleman, and stare thoughtfully out the window, or he would take a little nap himself.

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 eye was on him as he began to speak.

Every few minutes she would awaken for a moment to review things: Stowey, yes, was on his way south, and the two boys were away in school, and nothing was burning on the stove, and Lucretia was coming for dinner and bringing three guests of hers.

Every night they all went to Mama and Papa Albright's, and sat on the open front porch, where they could get the breeze.

Every single problem touched on thus far is related to good marketing planning.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

Every decision was made quickly on sound grounds.

Every night when he wanted a drink of water, didn't he practice being fearless by not turning on the bathroom light??

Every single instance of altruistic behavior need not always increase inclusive fitness ; altruistic behaviors would have been selected for if such behaviors on average increased inclusive fitness in the ancestral environment.

* 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 year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every actor who has opened in the role of Pseudolus on Broadway ( Zero Mostel, Phil Silvers and Nathan Lane ) won a Best Actor Tony Award for their performance.

* 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 cladogram is based on a particular dataset that was analyzed with a particular method.

Every year, the European Joint Conferences on Theory and Practice of Software ( ETAPS ) sponsors the International Conference on Compiler Construction ( CC ), with papers from both the academic and industrial sectors.

Every Halloween, Dabney House conducts the infamous " Millikan pumpkin-drop experiment " from the top of Millikan Library, the highest point on campus.

# Every net on X has a convergent subnet ( see the article on nets for a proof ).

# Every filter on X has a convergent refinement.

# Every ultrafilter on X converges to at least one point.

* Pseudocompact: Every real-valued continuous function on the space is bounded.

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.