** 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.

** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.

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

Every non-empty totally ordered set is directed.

* Every non-empty set of left ideals of R, partially ordered by inclusion, has a maximal element with respect to set inclusion.

* Every non-empty Baire space is of second category in itself, and every intersection of countably many dense open subsets of X is non-empty, but the converse of neither of these is true, as is shown by the topological disjoint sum of the rationals and the unit interval 1.

# ( Accessibility Property ) Every non-empty feasible set X contains an element x such that X

Every non-empty file must have at least one fork, and depending on the file system, a file may have one or more other associated forks, which in turn may contain primary data integral to the file, or just metadata.

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 ridge arises as the intersection of two facets ( but the intersection of two facets need not be a ridge ).

* Every intersection of countably many dense open sets is dense.

Every outerplanar graph is a circle graph, the intersection graph of a set of chords of a circle.

Every outerplanar graph can be represented as an intersection graph of axis-aligned rectangles in the plane, so outerplanar graphs have boxicity at most two.

Every intersection with a state or US Highway on US 24 from the Indiana state line to I-475 at Toledo will be an interchange.

# Every local complete intersection ring is Gorenstein.

# Every regular local ring is a complete intersection ring, so is Gorenstein.

Every other interchange with major roads along the route ( Toorak, Burke, Tooronga and Warrigal Roads ) was an at-grade intersection controlled by traffic-lights, and because the road was constructed through residential areas, reduced speed limits were also enforced.

Every closed, orientable, connected 3-manifold is obtained by performing Dehn surgery on a link in the 3-sphere.

Every time I closed my eyes, I saw Gray Eyes rushing at me with a knife.

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 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 unit of length has a corresponding unit of area, namely the area of a square with the given side length.

* 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 Boolean algebra ( A, ∧, ∨) gives rise to a ring ( A, +, ·) by defining a + b := ( a ∧ ¬ b ) ∨ ( b ∧ ¬ a ) = ( a ∨ b ) ∧ ¬( a ∧ b ) ( this operation is called symmetric difference in the case of sets and XOR in the case of logic ) and a · b := a ∧ b. The zero element of this ring coincides with the 0 of the Boolean algebra ; the multiplicative identity element of the ring is the 1 of the Boolean algebra.

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 quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.

* Every commutative real unital Noetherian Banach algebra with no zero divisors is isomorphic to the real or complex numbers.

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

Every city expansion would imply a new circle ( canals together with town walls ).

Jimmy Hatlo's They'll Do It Every Time was often displayed in a two-panel format with the first panel showing some deceptive, pretentious, unwitting or scheming human behavior and the second panel revealing the truth of the situation.

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 play is subject to booth review with coaches only having one challenge.

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 three years since Earnhardt's death, someone associated with Earnhardt has won the Daytona 500 ( his son Dale Earnhardt, Jr. in 2004, Earnhardt's replacement Cup driver Kevin Harvick in 2007, and Earnhardt Ganassi's Jamie McMurray in 2010.

Every song they wrote was written with an eye toward giving it " deep hidden meaning " or D. H. M.

In Norse mythology, Draupnir ( Old Norse " the dripper ") is a gold ring possessed by the god Odin with the ability to multiply itself: Every ninth night eight new rings ' drip ' from Draupnir, each one of the same size and weight as the original.

Every system must have a class designated as " root ", with one of its creation procedures designated as " root procedure ".

Every year, hundreds of new titles are published in Esperanto along with music.

Every point in three-dimensional Euclidean space is determined by three coordinates.

Every improper rotation of three-dimensional Euclidean space is rotation followed by a reflection in a plane through the origin.