This establishes a bijection ( up to isomorphism ) between the class of all finite posets and the class of all finite distributive lattices.

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.

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.

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.

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.

The musician employing the serial technique of composition establishes a mathematical system of rotations that, once set in motion, determines the sequence of pitches and even of rhythms and intensities.

Church services are regulated by the Manual, the set of by-laws written by Eddy, that establishes the church organization and explains the duties and responsibilities of members, officers, practitioners, teachers and nurses ; and establishes rules for discipline and other aspects of church business.

This set is defined in the HTML 4. 0 DTD, which also establishes the syntax ( allowable sequences of characters ) that can produce a valid HTML document.

Brownson, who argued that, in a sense, three " constitutions " are involved: first the constitution of nature that includes all of what the Founders called " natural law "; second the constitution of society, an unwritten and commonly understood set of rules for the society formed by a social contract before it establishes a government ; by which it does establish the third, a constitution of government.

It establishes a set of regular correspondences between early Germanic stops and fricatives and the stop consonants of certain other centum Indo-European languages ( Grimm used mostly Latin and Greek for illustration ).

In The Truce at Bakura, set one day after the ending of Return of the Jedi, Leia establishes New Alderaan, a sanctuary for the destroyed planet's surviving inhabitants.

* Boundary survey: a survey that establishes boundaries of a parcel using its legal description, which typically involves the setting or restoration of monuments or markers at the corners or along the lines of the parcel, often in the form of iron rods, pipes, or concrete monuments in the ground, or nails set in concrete or asphalt.

By changing the way they paint, apply colour, texture, perspective, or the way they see shapes and ideas, the artist establishes a certain set of " rules ".

One can prove the compactness theorem using Gödel's completeness theorem, which establishes that a set of sentences is satisfiable if and only if no contradiction can be proven from it.

:* The subject's withdrawal from the handshake is arrested by this attention arousal, which establishes a waiting set, and expectancy.

In the U. S., landfills are regulated by the state's environmental agency that establishes minimum guidelines ; however, none of these standards may fall below those set by the United States Environmental Protection Agency ( EPA ).

A religion which evolves its own priesthood and establishes a set of laws and rules is likely to lose its charismatic character and move towards another type of authority.

The. hack games are set after. hack // Sign, a TV anime series that establishes the games ' setting, The World.

Chapter I establishes the general obligation of the states parties to uphold the rights set forth in the Convention to all persons under their jurisdiction, and to adapt their domestic laws to bring them into line with the Convention.

An episode set in 2091 (" Solar Sailors ") establishes that Marty's music becomes famous to Elvis-like proportions, as there are Marty impersonators mimicking his act on stage.

Registration of a domain name establishes a set of Start of Authority ( SOA ) records in the DNS servers of the parent domain, indicating the IP address ( or domain name ) of DNS servers that are authoritative for the domain.

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.

Maggin story set in a future New York City, where the Silver Age Luthor establishes it after he is reformed.

The conceptual data model is the highest level ER model in that it contains the least granular detail but establishes the overall scope of what is to be included within the model set.

Post's theorem establishes a close connection between the arithmetical hierarchy and the Turing degrees of the form, that is, finitely iterated Turing jumps of the empty set.

The Japanese and European versions are nearly identical, but the American version changes the game's plot by adding an opening text that establishes the game to be set inside a giant alien life-form which is infected by a strain of bacteria.

It also establishes a set of principles to ensure the provision of a continuous riverside cycle / walkway, and the high quality design of new public open spaces and other infrastructure.