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establishes and bijection
This establishes a bijection between the set of all such digit-strings and the set of non-negative integers, avoiding the non-uniqueness caused by leading zeros.
Another version of this result, due to Peter J. Huber, establishes a bijection with the n-th &# 268 ; ech cohomology group when X is Hausdorff and paracompact and G is countable, or when X is Hausdorff, paracompact and compactly generated and G is arbitrary.
A further result of Morita establishes a bijection with the n-th numerable &# 268 ; ech cohomology group for an arbitrary topological space X and G an arbitrary abelian group.
Bijective numeration is any numeral system that establishes a bijection between the set of non-negative integers and the set of finite strings over a finite set of digits.

establishes and up
The introduction establishes that the game picks up right after the events of Duke Nukem II, with Duke returning to Earth in his space cruiser.
An establishing shot in filmmaking and television production sets up, or establishes the context for a scene by showing the relationship between its important figures and objects.
In doing so, he establishes a significant turn in the development of phenomenology, indicating that its conceptualisations should be re-examined in the light of the primacy of perception, in weighing up the philosophical consequences of this thesis.
He also establishes the many instances that Christianity and Judaism require us to give up our God-given reason in order to accept their claims to revelation.
The fundamental theorem of arithmetic establishes the central role of primes in number theory: any integer greater than 1 can be expressed as a product of primes that is unique up to ordering.
This organ draws up rules and ordinances, establishes municipal taxes, approves the budget and the accounts of the municipality, scrutinises the local services, and looks after the interests of its population in general ( spatial planning, road building, security, health, youth, sport ,...).
Adult numbats are solitary and territorial ; an individual male or female establishes a territory of up to 1. 5 square kilometres ( 370 acres ) early in life, and defends it from others of the same sex.
Also non-canon, David Mack's 2010 Star Trek: Typhon Pact novel, Zero Sum Game, establishes that the Breen Confederacy is made up of many separate species, all of which wear suits to disguise their appearances and subsume their identities into the Breen name.
After spending most of his life in a nomadic existence " up and down the dial ", WKRP settles Johnny down and establishes a relatively stable ensemble of friends and associates for him.
In other words, a PCT application, which establishes a filing date in all contracting states, must be followed up with the step of entering into national or regional phases in order to proceed towards grant of one or more patents.
The tendency of the one to speak up and the other to be silent starts off a spiraling process which increasingly establishes one opinion as the dominant one.
Further, another story within the story arc establishes the Spacers ' mastery of myco-food ( food derived from fungi ), which they then retain all through history up to their inclusion in the Imperium on Trantor in the sector of Mycogen.
The first clause establishes suspense about who actually rules the ghetto, and then the first few words of the second clause set up the reader with the expectation of an answer, which is metaphorically revealed only in the final word of the sentence.
As Sherban grows up he establishes contact with other Canopeans in disguise and then resumes his work trying to help the Shikastans.
from: 16 / 07 / 1998 till: 16 / 07 / 1998 color: LAB $ right text :" 16th July 1998-Teaching and Higher Education Act passed into law ~ establishes tuition fees of up to £ 1000 "
Article 3 forbids the setting up of a list of prohibited books and establishes the bases for a free, mandatory, and lay education ; article 27 led the foundation for land reforms ; and article 123 was designed to empower the labor sector.
As Buffy establishes herself in school in early episodes, Joyce, who is recently divorced, is preoccupied with setting up their home and running an art gallery.
* This episode establishes that vampires show up on film, despite the fact that they have no reflections.
The first episode of the fourth season, in which a 40-something Becca ( played by Pamela Bellwood ) tours the house she grew up in while remembering the events of twenty-five years earlier, establishes that Jesse would ultimately die from AIDS, and that Becca would move on and marry a man named David.
Aristarchus's " hyper-criticism " establishes a science for the mock heroic and follows up some of the ideas set forth by Pope in Peri Bathos in the Miscellanies, Volume the Third ( 1727 ).
It also sets up a multilateral priority filing system, under which an application for protection filed in one member state establishes a filing date for applications filed in all other member states within one year of that original filing date.
Some newer versions of pppd are also capable of handling Dial-on-demand routing, where pppd sets up a virtual network, captures the packages it receives and establishes a PPP connection and forwards the captured and not-yet transmitted packages over the link.
In the latter work Lazarus takes ethics as the resultant rather than as the basic principle of religion, and, following Kant, establishes as the principle of Jewish ethics in particular the co-equality of God and the law of autonomy, whereby the Jewish conception of God has, of course, been given up.
This establishes the up and down directions.

establishes and isomorphism
Regardless of the definition, Taylor's theorem establishes a canonical isomorphism of vector spaces between and.

establishes and between
It is the similarity between Estella's hands and Molly's ( `` The action of her fingers was like the action of knitting '' ) that provides Pip with a vital clue to the real identity of both and establishes a symbolic connection between the underworld of crime and the genteel cruelty of Satis House.
Administrative law in Germany, called “ Verwaltungsrecht ”: de: Verwaltungsrecht ( Deutschland ), generally rules the relationship between authorities and the citizens and therefore, it establishes citizens ’ rights and obligations against the
The constitution, adopted by referendum in 2005, and promulgated by President Joseph Kabila in February 2006, establishes a decentralized semi-presidential republic, with a separation of powers between the three branches of government-executive, legislative and judiciary, and a distribution of prerogatives between the central government and the provinces.
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the deep relationship between the trigonometric functions and the complex exponential function.
Language is particularly important, for it establishes a bridge between natural science and philosophy.
Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.
* 1846 – The Oregon Treaty establishes the 49th parallel as the border between the United States and Canada, from the Rocky Mountains to the Strait of Juan de Fuca.
Brazilian law establishes no difference between cities and towns ; all it takes for an urban settlement to be called a " city " is to be the seat of a municipality, and some are very small.
* 1677 – Treaty of Middle Plantation establishes peace between the Virginia colonists and the local Natives.
* 1795 – The United States and Spain sign the Treaty of Madrid, which establishes the boundaries between Spanish colonies and the U. S.
Supervenience establishes such a relationship between the mental and the physical, that any change in the mental is caused by a change in the physical.
A title, or a right of ownership, establishes the relation between the property and other persons, assuring the owner the right to dispose of the property as the owner sees fit.
This theorem establishes an important connection between a Hilbert space and its ( continuous ) dual space: if the underlying field is the real numbers, the two are isometrically isomorphic ; if the field is the complex numbers, the two are isometrically anti-isomorphic.
The treaty establishes rights and obligations between the Swiss and the EU and the member states severally ; it does not establish any rights and obligations amongst the EU and its member states.
The agreement establishes rights and obligations between each party and every other party.
* October 20 – Treaty between the U. S. and the United Kingdom establishes the boundary between the U. S. and British North America as the 49th parallel from the Lake of the Woods to the Rocky Mountains, also creating the Northwest Angle.
* December 11 – The British Parliament enacts the Statute of Westminster, which establishes a status of legislative equality between the self-governing dominions of the Commonwealth of Australia, the Dominion of Canada, the Irish Free State, Newfoundland, the Dominion of New Zealand, and the Union of South Africa.
The Battle of Tours halts the advance of Islam into Western Europe and establishes a balance of power between Western Europe, Islam and the Byzantine Empire.
* February 6 – A formal treaty between Hussein Shah of Johor and the British Sir Thomas Stamford Raffles establishes a trading settlement in Singapore.
* May 29 – The Treaty of Middle Plantation establishes peace between the Virginia colonists and the local Indians.

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