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.

** 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.

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

# Every infinite subset of X has a complete accumulation point.

# Every infinite subset of A has at least one limit point in A.

* Limit point compact: Every infinite subset has an accumulation point.

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 separable metric space is homeomorphic to a subset of the Hilbert cube.

* Every separable metric space is isometric to a subset of the ( non-separable ) Banach space l < sup >∞</ sup > of all bounded real sequences with the supremum norm ; this is known as the Fréchet embedding.

* Every separable metric space is isometric to a subset of C (), the separable Banach space of continuous functions → R, with the supremum norm.

* Every separable metric space is isometric to a subset of the

Every element s, except a possible greatest element, has a unique successor ( next element ), namely the least element of the subset of all elements greater than s. Every subset which has an upper bound has a least upper bound.

Every subset of a nowhere dense set is nowhere dense, and the union of finitely many nowhere dense sets is nowhere dense.

* Every subset of Baire space or Cantor space is an open set in the usual topology on the space.

* Every arithmetical subset of Cantor space of < sup >( or?

Every subset of the Hilbert cube inherits from the Hilbert cube the properties of being both metrizable ( and therefore T4 ) and second countable.

It is more interesting that the converse also holds: Every second countable T4 space is homeomorphic to a subset of the Hilbert cube.

* Every totally disconnected compact metric space is homeomorphic to a subset of a countable product of discrete spaces.

* Every irreducible closed subset of P < sup > n </ sup >( k ) of codimension one is a hypersurface ; i. e., the zero set of some homogeneous polynomial.

* Every finite or cofinite subset of the natural numbers is computable.

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.

* 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.

Disraeli wrote a personal letter to Gladstone, asking him to place the good of the party above personal animosity: " Every man performs his office, and there is a Power, greater than ourselves, that disposes of all this ..." In responding to Disraeli Gladstone denied that personal feelings played any role in his decision then and previously to accept office, while acknowledging that there were differences between him and Derby " broader than you may have supposed.

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.

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 ".

Cobham was a common butt of veiled satire in Elizabethan popular literature ; he figures in Ben Jonson's Every Man in His Humour and may have been part of the reason The Isle of Dogs was suppressed.

Every convict detained in a TBS-clinic may get temporary leave, after serving a certain time or after some progress in treatment.

Every key frame is numbered with a multi-digit identifier that may be referred to later.

Every RFC is submitted as plain ASCII text and is published in that form, but may also be available in other formats.

The last two lines of the Act IV-scene 2 funeral song may also have inspired the lines W. H. Auden, the librettist for Stravinsky's The Rake's Progress, puts into the mouth of Anne Truelove at the end of the opera: " Every wearied body must late or soon return to dust ".

Every compact Hausdorff space is also locally compact, and many examples of compact spaces may be found in the article compact space.

*: Articles 19 and 23 of the constitution provides, " Every person of I-Kiribati descent ... shall ... become or have and continue to have thereafter the right to become a citizen of Kiribati .... Every person of I-Kiribati descent who does not become a citizen of Kiribati on Independence Day ... shall, at any time thereafter, be entitled upon making application in such manner as may be prescribed to be registered as a citizen of Kiribati.

Every first Friday of the month, a trolley travels around Washington Street at different cafes and shops as artists showcase different pieces and may include auctions. This neighboorhod is scattered with urban blight ( within the residential section, from Caroll St east to the Brandywine Highway ).

Every point constructible using straightedge and compass may be constructed using compass alone.

Every non-inner automorphism yields a non-trivial element of Out ( G ), but different non-inner automorphisms may yield the same element of Out ( G ).

Every governing body is free to set its own standards, so the quality of races may differ.

Every gap sequence that contains 1 yields a correct sort ; however, the properties of thus obtained versions of Shellsort may be very different.

Every Dean of the Faculty ( equivalent to a Provost at most universities ) has always been an active-duty brigadier general, although technically, a civilian may hold the position.

The directive declared, " Every military commander has the responsibility to oppose discriminatory practices affecting his men and their dependents and to foster equal opportunity for them, not only in areas under his immediate control, but also in nearby communities where they may live or gather in off-duty hours.

From the Constitution of Lithuania, Article 32 ( 4 ): " Every Lithuanian person may settle in Lithuania.

Every kid is rated in running, batting, fielding, and pitching and has personality quirks that may affect the team.

Every late July ( ending on the last Saturday of July and beginning 10 days previous ) it hosts what may be the world's largest free-admission fair.

Every star of this type may usually be assigned a certain mean period.

Every 5 years the JNCC coordinates a compulsory review of schedules 5 and 8 to add new species that may need protection ( Legislation. gov. uk, 2010 ).