* Given any topological space X, the continuous real-or complex-valued functions on X form a real or complex unitary associative algebra ; here the functions are added and multiplied pointwise.

Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ).

Given the complexity of the calculations involved and the convoluted structure that a convertible bond can have, an arbitrageur often relies on sophisticated quantitative models in order to identify bonds that are trading cheap versus their theoretical value.

Given that Bozizé accuses Sudan of supporting the UFDR rebels who are actively fighting the Central African Government, the relation between the two countries has remained good.

Given this popular understanding of the term, it can also be used illegitimately and inappropriately, as a means to dismiss what are in fact substantial and well-evidenced accusations.

Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.

Given the rugged terrain of Ngazidja and Nzwani, and the dedication of extensive tracts to agriculture on all three islands, population pressures on Comoros are becoming increasingly critical.

Given this basic definition, further criteria are needed to establish a dividing line between postlexical clitics and morphological affixes, since both are characterized by a lack of prosodic autonomy.

Given that a father's age is 1 less than twice that of his son, and that the digits AB making up the father's age are reversed in the son's age ( i. e. BA ), leads to the equation 19B-8A

Given its different forms, there are various ways of representing uncertainty and modelling economic agents ' responses to it.

* Given a partition of A, G is a transformation group under composition, whose orbits are the cells of the partition ‡;

* Given a transformation group G over A, there exists an equivalence relation ~ over A, whose equivalence classes are the orbits of G.

Raymond also coined an aphorism he dubbed " Linus ' Law ", inspired by Linus Torvalds: " Given enough eyeballs, all bugs are shallow ", that first appeared in The Cathedral and the Bazaar.

Given the great historical link between Persian and Jewish history, modern day Persian Jews are called " Esther's Children ".

Given that the vast majority of all emeralds are treated as described above, and the fact that two stones that appear visually similar may actually be quite far apart in treatment level and therefore in value, a consumer considering a purchase of an expensive emerald is well advised to insist upon a treatment report from a reputable gemological laboratory.

Given the difficulty of finding exact solutions, Einstein's field equations are also solved frequently by numerical integration on a computer, or by considering small perturbations of exact solutions.

Given a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

Given that genes are universal to living organisms, genetics can be applied to the study of all living systems, from viruses and bacteria, through plants and domestic animals, to humans ( as in medical genetics ).

Given a groupoid G, the vertex groups or isotropy groups or object groups in G are the subsets of the form G ( x, x ), where x is any object of G. It follows easily from the axioms above that these are indeed groups, as every pair of elements is composable and inverses are in the same vertex group.

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.

Given that the coiled texture is the natural state of some African Americans ' hair, or perceived as being more " African ", this simple style is now often seen as a sign of self-acceptance and an affirmation that the beauty norms of the ( eurocentric ) dominant culture are not absolute.

Given these two assumptions, the coordinates of the same event ( a point in space and time ) described in two inertial reference frames are related by a Galilean transformation.

Given the difficulty of this position, it is not uncommon for the best player on the team to play Number Two so long as another strong player is available to play Three.

Given that the authors were the primary developers of the Unix operating system, it is natural that QED had a strong influence on the classic UNIX text editors ed, sed and their descendants such as ex and sam.

* Given their strong position, the mercenaries inflate their demands and demand payment for the non-mercenary Libyan conscripts in the army as well.

Given that France maintained a strong standing army, and that Prussia and the other German states would need weeks to mobilise their conscript armies, the French held the initial advantage of troop numbers and experience.

Given Switzerland's particularly strong opinions on who is " Swiss " and who is " other ", it is easy to see that groups such as Stoffunita make use of the fact that hip hop " is still considered a voice for the oppressed " as hip hop scholar and author Jeff Chang notes.

Given the inexperience of the WP team and Lee Hsien Loong's position as the Prime Minister, they won a surprisingly strong 49, 468 votes ( 30. 94 %).

Given that the number of women needing to travel has doubled since 1995, there is a very strong demand for these kinds of services.

Given her husband's weak physical and mental condition, she exerted a strong influence on imperial life, and was an active patron of Japanese Red Cross Society.

Given the relatively strong historical record running alongside the archaeological one, post-medieval archaeology is often better positioned to study the effects of known social and political change.

Given this strong theme in the film, the title was soon changed from Vigilance to Magnum Force in deference to the. 44 Magnum that Harry liked to use.

Given the countably infinite number of ways of forming mathematical expressions using a finite number of symbols, the number of symbols used and the precision of approximate equality might be the most obvious way to assess mathematical coincidences ; but there is no standard, and the strong law of small numbers is the sort of thing one has to appeal to with no formal opposing mathematical guidance.

Given his strong interest in astronomy, Oriani was appointed on the staff of the Observatory of Brera in Milan in 1776, becoming assistant astronomer in 1778 and director in 1802.

Given Australia has a population of only around 20 million people ( ranked 53rd in the world ) this fact is frequently cited as noteworthy by the mainstream Australia media due to a strong sporting culture.

Given recent comebacks such as The Miracle at the New Meadowlands ( where the Philadelphia Eagles won by scoring 28 points in the last 7 minutes ) and how quickly points can be accumulated ( through interception returns, onside kicks and kick returns ) it is understandable that coaches are cautious about becoming overconfident in their offenses and they normally prefer to run out the clock rather than risk an unlikely but certainly possible comeback late in the game, particularly for teams who have a strong offence but a weaker defense.

Given the fact that waves start to break against the rock on a good day, and that a strong riptide along the promontory creates a quick re-entry, the take-off point is very small and only locals ( or visiting professional-level surfers ) have a shot at it.

Given that gratitude appears to be a strong determinant of people's well-being, several psychological interventions have been developed to increase gratitude.

Given these properties, it is not surprising that a strong correlation between Wnt signaling and the onset of cancer exists.

Given the strong political parties of the Third Party System, the leading politicians controlled enough support in state legislatures to be elected Senators.

Given the strength of the Labour presence in the European socialist movement — the 1994 elections in the UK gave Labour 61 seats, and nearly a third of the 15 party Socialist Group — they were in a strong position to get what they wanted.

“ Given that I was born a few months after Auschwitz was liberated, it is hardly surprising that I have a strong sense of the evil that humans – individually and collectively – do.

Given strong mental blocks to inhibit their powers, the Martians assumed normal Earth lives all over the globe, although they were kept under observation by the League.

Given a dual pair the strong topology on is the polar topology defined by using the family of all sets in where the polar set in is absorbent.

Given that the North Shore portions of the riding were largely affluent and upper middle class in character and normally a Liberal bastion, Douglas ' strong showing is not so surprising given the working-class and labour background of much of even the better-off parts of the riding in Burnaby.

Given the strong medieval trade connections between south-east England and the County of Flanders when the latter belonged to the Duchy of Burgundy, the name may have been derived from the Middle Dutch krick (- e ), meaning a stick ; or the Olde English cricc or cryce meaning a crutch or staff.