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.

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 aspect of his architecture, from overall concept to the smallest detail, supports his effort to express the modern age.

Every point of X has a smallest neighbourhood.

Every domain D can be embedded in an ω-complete domain completion ( called the ω-completion or simply the completion of D ) that is, in a precise sense, the smallest ω-complete domain containing D. The isolated elements of completion are precisely the isolated elements of D, but in general completion contains limit points that are not found in D. completion is uniquely determined up to isomorphism.

Every student is continuously evaluated, corrected, and mentored, with special attention paid to the smallest of details, such as the placement of a finger within 1 / 4 inch of its required location along a trouser seam, angle of the weapon, and positioning of the student in relation to the unit.

Every February and March, professional and recreational racers put their minds, muscles and machines to work in epic long-distance winter races that link Alaska's largest and smallest communities.

Every part, to the smallest bits, is magnificently played ..."

Every smaller cubic graph has shorter cycles, so this graph is the 6-cage, the smallest cubic graph of girth 6.

Every level of the building has been renovated ( back to its original 1929 state ) down to the smallest details such as the clocks on the walls and the " showcases " in the area now occupied by the library.

Every section of the media should get the same attention from me, from the capital's most prominent TV channel to the smallest newspaper in the provinces.

Every movement she made seemed unnecessarily noisy.

Every recorded request by Thomas for a delay in a flank movement or an advance was to gain time to take care of his horses.

Historian Barry Adam notes, " Every social movement must choose at some point what to retain and what to reject out of its past.

Every game in the main Zelda series has consisted of three principal areas: an overworld in which movement is multidirectional, allowing the player some degree of freedom of action ; areas of interaction with other characters ( merely caves or hidden rooms in the first game, but expanding to entire towns and cities in subsequent games ) in which the player gains special items or advice ; and dungeons, areas of labyrinthine layout, usually underground, comprising a wide range of difficult enemies, bosses, and items.

From a pro-independence supporter's point of view, the movement for Taiwan independence began under Qing rule in the 1680s which led to a well known saying those days, " Every three years an uprising, every five years a rebellion ".

Every movement, reflex, facial expression, and reaction is measured by this system, monitored by the Ministry of Love.

Every practice of the infant's movement intended to advance the integration of behavior favourable to development in the experimental framework appeared to be selected from an excess of movement in the trial of imitation.

Every castle she lived in was equipped with a gymnasium, the Knights ' Hall of the Hofburg was converted into one, mats and balance beams were installed in her bedchamber so that she could practice on them each morning, and the imperial villa at Ischl was fitted with gigantic mirrors so that she could correct every movement and position.

Every house system is dependent on the rotational movement of Earth on its axis, but there is a wide range of approaches to calculating house divisions and different opinions among astrologers over which house system is most accurate.

Every evening they fly, often in groups and sometimes over long distances, to reach safe roosting sites such as dense trees or shrubs that impede predator movement, or, at higher latitudes, dense conifers that afford good wind protection.

She is best known as a chronicler of the movement's spread, especially in her 1884 Nineteenth Century Miracles: Spirits and their Work in Every Country of the Earth, and her 1870 Modern American Spiritualism, a detailed account of claims and investigations of mediumship beginning with the earliest days of the movement.

Every major movement in Western history has been accompanied by its own collection of protest songs, from slave emancipation to women's suffrage, the labor movement, civil rights, the anti-war movement, the feminist movement, the environmental movement.

Every July 25, Puerto Rican Nationalists and independence activists gather on Cerro Maravilla to honor Carlos Soto and Arnaldo Dario, as well as to defend and celebrate the Puerto Rican independence movement.

Every movement in the katas has a function.

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.

The official slogan of the Share The Wealth movement was " Every Man a King ( But No One Wears a Crown )", which also became the title of a song co-written by Long in 1935 to promote his proposal.

Every movement but the third is in sonata form ; the minuet and trio are in the usual ternary form.

Every movement except the minuet is in sonata form.

Every day our leadership would listen to world news over the radio at 9 a. m. to follow the growth of the American antiwar movement.

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.