Every element of is a member of the equivalence class.

Every two equivalence classes and are either equal or disjoint.

Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes ( or congruence classes ) for the relation.

Every adjunction 〈 F, G, ε, η 〉 extends an equivalence of certain subcategories.

Every homeomorphism is a homotopy equivalence, but the converse is not true: for example, a solid disk is not homeomorphic to a single point, although the disk and the point are homotopy equivalent.

Every commodity is listed separately, and there is never any sign of equivalence between one unit and another.

Every ordered basis lives in one equivalence class or another.

* Every homotopy equivalence between two Hilbert manifolds is homotopic to a diffeomorphism.

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

* Every free abelian group is torsion-free, but the converse is not true, as is shown by the additive group of the rational numbers Q.

Every algebraic curve C of genus g ≥ 1 is associated with an abelian variety J of dimension g, by means of an analytic map of C into J.

Every free abelian group has a rank defined as the cardinality of a basis.

Every subgroup of a free abelian group is itself free abelian, which is important for the description of a general abelian group as a cokernel of a homomorphism between free abelian groups.

* Every cyclic group is locally cyclic, and every locally cyclic group is abelian.

* Every abelian group can be embedded in a divisible group.

A finitely-generated abelian group is indecomposable if and only if it is isomorphic to Z or to a factor group of the form for some prime number p and some positive integer n. Every finitely-generated abelian group is a direct sum of ( finitely many ) indecomposable abelian groups.

Every abelian category is an exact category if we just use the standard interpretation of " exact ".

Every sentence must contain formal words to designate what Husserl calls " formal categories ".

Every functor induces the opposite functor, where and are the opposite categories to and.

Every human action belongs in one of these five categories.

Every six months member countries exchange information on deliveries of conventional arms to non Wassenaar members that fall under eight broad weapons categories: battle tanks, armored combat vehicles ( ACVs ), large-caliber artillery, military aircraft / unmanned aerial vehicles, military and attack helicopters, warships, missiles or missile systems, and small arms and light weapons.

" Every Breath You Take " also won the American Video Award for " Best Group video " and nabbed two Ivor Novello Awards for the categories " Best Song Musically and Lyrically " and " Most Performed Work ".

Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories.

Every pre-abelian category is of course an additive category, and many basic properties of these categories are described under that subject.

Every person born into this world comes from one of these categories in order to help fulfill the kind of function that that category of people is supposed to fulfill in order to keep the community together.

Every year a chapter is selected as chapter of the year ; this is the chapter which has received the highest overall scores in all hallmark categories.

Every year, the number of entries from the previous year is beaten, as more categories and a wider selection of issues are taken into account.

Every test can be added to one or more categories, to allow running them selectively.

Every group, every three months, is given budgets of varying amounts in each the following categories: Cultural Discovery, Environment, Healthy Life Style, Second Languages and Leadership.

Every character's categories may be customized before starting the race.

Every year the Guide presents its Editor's Awards in the following categories ; Best New Entry, Best Pub Newcomer, Wine List of the Year, Best Chef, Best Up-and-Coming Chef, Best Pub Chef, Best Fish Restaurant, Best Value for Money, Best Use of Local Produce, and Best Family Restaurant.

Every year the ICP holds an international conference to promote 45 categories within psychological science and raise awareness about the applications they can bring to our lives.

Every year they invite scientists to contribute videos and offer awards in various categories.

Every country has their own way of organizing the work of IAESTE, but the National Committee can mainly be classified in four categories:

Every type of land having one Khanduga of sowing capacity was taken as a measuring unit and the highest and lowest rates for that unit were fixed for each of the five categories.

Every year designers and corporations submit entries into the competition in many categories.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

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 taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

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 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 man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

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 lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.