: Every set has a choice function.

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.

** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.

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

** Antichain principle: Every partially ordered set has a maximal antichain.

* 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 non-empty set A contains an element B which is disjoint from A.

* 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 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 cofinal subset of a partially ordered set must contain all maximal elements of that set.

Every corporation, whether financial or union, as well as every division of the administration, were set up as branches of the party, the CEOs, Union leaders, and division directors being sworn-in as section presidents of the party.

Every DNS zone must be assigned a set of authoritative name servers that are installed in NS records in the parent zone, and should be installed ( to be authoritative records ) as self-referential NS records on the authoritative name servers.

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.

# " Personality " Argument: this argument is based on a quote from Hegel: " Every man has the right to turn his will upon a thing or make the thing an object of his will, that is to say, to set aside the mere thing and recreate it as his own ".

Every atom across this plane has an individual set of emission cones .</ p > < p > Drawing the billions of overlapping cones is impossible, so this is a simplified diagram showing the extents of all the emission cones combined.

* Every singleton set

Every processor or processor family has its own machine code instruction set.

Every set is a class, no matter which foundation is chosen.

Every non-empty totally ordered set is directed.

* Every preorder can be given a topology, the Alexandrov topology ; and indeed, every preorder on a set is in one-to-one correspondence with an Alexandrov topology on that set.

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 adiabat asymptotically approaches both the V axis and the P axis ( just like isotherms ).

Every seminorm on V ( in particular, every norm on V ) is sublinear.

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 pope from Miltiades occupied the Lateran Palace until the reign of the French Pope Clement V, who in 1309 decided to transfer the official seat of the Catholic Church to Avignon, a papal fief that was an enclave within France.

Every measurable cardinal κ is a 0-huge cardinal because < sup > κ </ sup > M ⊂ M, that is, every function from κ to M is in M. Consequently, V < sub > κ + 1 </ sub >⊂ M.

* Every cover is a local homeomorphism — that is, for every, there exists a neighborhood of c and a neighborhood of such that the restriction of p to U yields a homeomorphism from U to V. This implies that C and X share all local properties.

Every graph has a harmonious coloring, since it suffices to assign every vertex a distinct color ; thus χ < sub > H </ sub >( G ) ≤ | V ( G )|.

Indeed, in a 2011 review of " I Want My MTV " by Craig Marks and Rob Tannenbaum, Dwight Garner recalled: " Every sentient straight male in the country developed a schoolboy crush on Martha Quinn, one of the first V. J.

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 )

Iris Adrian was an only child, raised by a single mother, Florence V. Hostetter ( née Every ), in Los Angeles, California.

Every year, the Blue Cross Arena hosts regular season Section V high school hockey games and the Section V Basketball championship.

When a variable, v, is on the LHS of an assignment statement, such as s ( j ), then s ( j ) is a definition of v. Every variable ( v ) has at least one definition by its declaration ( V ) ( or initialization ).

Every element of naturally corresponds the subset of V which assigns a 1 to its vertices.

King's Quest V also inspired a text based remake, King's Quest V-The Text Aventure, and also another parody fan-game Owl's Quest: Every Owl has it's Day starring Cedric which pokes fun of many of the situations and mannerisms of Cedric.

Every Man Out of His Humour includes several references to Shakespeare and his contemporaneous works: a mention of Justice Silence from Henry IV, Part 2 —" this is a kinsman to Justice Silence " ( V, ii ) and two allusions to Julius Casear, which help to date that play to 1599.

" Et tu, Brute " occurs in V, iv of Every Man Out ; in III, i appears " reason long since is fled to animals ," a paraphrase of Shakespeare's line " O judgment, thou art fled to brutish beasts " in Julius Caesar, III, ii, 104.

Every state except Hawaii has applied for an Article V convention at one time or another.

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.

** 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.