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Extension (other)
Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * Extension (semantics), the set of things to which a property applies * Extension by definitions * Extensional definition, a definition that enumerates every individual a term applies to * Extensionality Other uses * Extension of a function, defined on a larger domain * Extension of a polyhedron, in geometry * Exterior algebra, Grassmann's theory of extension, in geometry * Field extension, in Galois theory * Group extension, in abstract algebra and homological algebra * Homotopy extension property, in topology * Kolmogorov extension theorem, in probability theory * Linear extension, in order theory * Sheaf extension, in algebraic geometry * Tietze extension theorem, in topology * Whitney extension theorem, in differential geometry M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiom Of Extensionality
In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo–Fraenkel set theory. It says that sets having the same elements are the same set. Formal statement In the formal language of the Zermelo–Fraenkel axioms, the axiom reads: :\forall A \, \forall B \, ( \forall X \, (X \in A \iff X \in B) \implies A = B) or in words: : Given any set ''A'' and any set ''B'', if for every set ''X'', ''X'' is a member of ''A'' if and only if ''X'' is a member of ''B'', then ''A'' is equal to ''B''. :(It is not really essential that ''X'' here be a ''set'' — but in ZF, everything is. See Ur-elements below for when this is violated.) The converse, \forall A \, \forall B \, (A = B \implies \forall X \, (X \in A \iff X \in B) ), of this axiom follows from the substitution property of equality. Interpretation To understand this axiom, note that the clau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tietze Extension Theorem
In topology, the Tietze extension theorem (also known as the Tietze–Urysohn–Brouwer extension theorem) states that continuous functions on a closed subset of a normal topological space can be extended to the entire space, preserving boundedness if necessary. Formal statement If X is a normal space and f : A \to \R is a continuous map from a closed subset A of X into the real numbers \R carrying the standard topology, then there exists a of f to X; that is, there exists a map F : X \to \R continuous on all of X with F(a) = f(a) for all a \in A. Moreover, F may be chosen such that \sup \ ~=~ \sup \, that is, if f is bounded then F may be chosen to be bounded (with the same bound as f). History L. E. J. Brouwer and Henri Lebesgue proved a special case of the theorem, when X is a finite-dimensional real vector space. Heinrich Tietze extended it to all metric spaces, and Pavel Urysohn proved the theorem as stated here, for normal topological spaces. Equivalent statements Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension, Louisiana
Extension is an unincorporated community in Franklin Parish, Louisiana, United States. Its ZIP code is 71243. Notable people Singer and songwriter Richard Berry was born in Extension. He is known for writing one of the world's most recorded songs, "Louie Louie "Louie Louie" is a rhythm and blues song written and composed by American musician Richard Berry in 1955, recorded in 1956, and released in 1957. It is best known for the 1963 hit version by the Kingsmen and has become a standard in pop and ...." Notes Unincorporated communities in Franklin Parish, Louisiana Unincorporated communities in Louisiana {{Louisiana-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension, British Columbia
Extension is an unincorporated community near the east coast of southern Vancouver Island, British Columbia. The location off BC Highway 19 is about by road northwest of Victoria, and south of Nanaimo. Discovery Louis Stark, an African American, lived in today's Colvilletown neighbourhood of south Nanaimo. Many suspected foul play when his body was found at the bottom of a cliff in 1895. One theory claimed he had refused to sell his coal rich land to Dunsmuir coal, desperately seeking new sources to replace its nearly exhausted Wellington mine. Another rumour suggested he was the discoverer of the coal seam on the southern slope of Mt. Benson. However, after the death, his close neighbour Ephraim (Edward) Hodgson claimed the credit and reward for the discovery. Murder charges against Hodgson were dropped. The Mt. Benson seam proved to be an extension of the Wellington one being worked by Dunsmuir, and the location was initially called Wellington Extension. Railway Thwarted ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kylie Minogue
Kylie Ann Minogue (; born 28 May 1968) is an Australian singer, songwriter and actress. She is the highest-selling female Australian artist of all time, having sold over 80 million records worldwide. She has been recognised for reinventing herself in music and fashion, for which she is referred to by the European press as the "Princess of Pop" and a style icon. Her accolades include a Grammy Award, three Brit Awards and 17 ARIA Music Awards. Born and raised in Melbourne, Minogue first achieved recognition starring in the Australian soap opera '' Neighbours'', playing tomboy mechanic Charlene Robinson. She gained prominence as a recording artist in the late 1980s and released four bubblegum and dance-pop-influenced studio albums produced by Stock Aitken Waterman. By the early 1990s, she had amassed several top ten singles in the UK and Australia, including " I Should Be So Lucky", " The Loco-Motion", " Hand on Your Heart", and " Better the Devil You Know". Taking m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (The Manhattan Transfer Album)
Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * Extension (semantics), the set of things to which a property applies * Extension by definitions * Extensional definition, a definition that enumerates every individual a term applies to * Extensionality Other uses * Extension of a polyhedron, in geometry * Exterior algebra, Grassmann's theory of extension, in geometry * Homotopy extension property, in topology * Kolmogorov extension theorem, in probability theory * Linear extension, in order theory * Sheaf extension, in algebraic geometry * Tietze extension theorem, in topology * Whitney extension theorem, in differential geometry * Group extension, in abstract algebra and homological algebra Music * Extension (music), notes that fit outside the standard range * ''Extended'' (Solar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (Dave Holland Album)
''Extensions'' is an album by jazz bassist Dave Holland released on the ECM label in 1990. The record is Dave Holland's eighth album to be released on the ECM label. It features two members of his previous quintet— saxophonist Steve Coleman and drummer Marvin "Smitty" Smith—alongside guitarist Kevin Eubanks, in his first appearance on a Holland record. Holland recorded "Processional" again on his later sextet album ''Pass It On''. Reception The Allmusic review by Brian Olewnick awarded the album 4 stars, calling it a "tight and enjoyable quartet date" and "One of his better albums from this period, ''Extensions'' should please any Holland fan, and is an agreeable and non-threatening jumping in point for the curious".Olewnick, BAllmusic Reviewaccessed August 19, 2011. ''Extensions'' was voted Album of the Year (1989) by '' Downbeat Magazine''. Track listing # "Nemesis" (Kevin Eubanks) - 11:31 # "Processional" (Dave Holland) - 7:16 # "Black Hole" (Steve Coleman) - 10:10 # ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (McCoy Tyner Album)
''Extensions'' is an album by jazz pianist McCoy Tyner released on the Blue Note label. It was recorded on February 9, 1970 but not released until January of 1973. It has performances by Tyner with alto saxophonist Gary Bartz, tenor saxophonist Wayne Shorter, bassist Ron Carter, drummer Elvin Jones, and features Alice Coltrane playing harp on three of the four tracks. Reception In his AllMusic review Scott Yanow says, "The all-star sextet stretches out on lengthy renditions of four of Tyner's modal originals, and there is strong solo space for the leader and the two saxophonists... Stimulating music". Reviewing the album for jazz.com, Jared Pauley says, "McCoy Tyner finds himself among elite company on ''Extensions.'' Recorded as jazz was entering the fusion period, this is a great example of just how good straight-ahead swing can sound... This performance matches the superb quality of previous Shorter and Tyner albums where members of the Davis and Coltrane groups recorded ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mystic Moods Orchestra
The Mystic Moods Orchestra was a group known for mixing orchestral pop, environmental sounds, and pioneering recording techniques. It was created by audiophile Brad Miller. The first Mystic Moods Orchestra album, ''One Stormy Night'', was released in 1966 through the label Philips. Throughout the rest of the 1960s and 1970s, the group continued to release similar styled recordings and their recordings continued to be reissued throughout the 1980s and 1990s. History Brad Miller was born in Burbank, California Burbank is a city in the southeastern end of the San Fernando Valley in Los Angeles County, California, United States. Located northwest of downtown Los Angeles, Burbank has a population of 107,337. The city was named after David Burbank, wh ..., and had developed an interest in railroading in his teens. After a few years of hanging around railyards and learning all the lore of steam and diesel engines, he decided to record the sounds of some of the last steam locomotiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extensions (Ahmad Jamal Album)
''Extensions'' is an album by American jazz pianist Ahmad Jamal featuring performances recorded in 1965 and released on the Argo label.Ahmad Jamal discography accessed May 18, 2012 Critical reception awarded the album 3 stars.Allmusic Reviewaccessed May 18, 20121 Track listing # "Extensions" (Ahmad Jamal) – 13:10 # "Dance to the Lady" () – 5:50 # "Thi ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension (Clare Fischer Album)
''Extension'' is the third album by composer/arranger/keyboardist Clare Fischer, and his first for big band, recorded and released in 1963 on the Pacific Jazz label, reissued on CD (together with the 1967 LP, ''Songs for Rainy Day Lovers'') in 2002 as ''America the Beautiful'', and, under its original name, in 2012. WorldCat. Retrieved 2013-03-18 According to Ed Beach, disk jockey of the WRVR 106.7 FM New York radio program “Just Jazz,” on this album, all of the solos, except for those of Clare Fischer and tenor saxophonist Jerry Coker, were written out (by Fischer), not improvised. Reception Reviewing the 2012 CD reissue for All About Jazz, Troy Collins calls ''Extension'' Fischer's "mas ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extension (George Braith Album)
''Extension'' is the third album by American saxophonist George Braith recorded in 1964 and released on the Blue Note label.Blue Note Records discography accessed November 17, 2010 Reception The review by Stephen Thomas Erlewine awarded the album 4½ stars and stated "George Braith turned in his strongest record with ''Extension''. Largely freed from the restraints of the dueling horns, Braith is able to explore the outer reaches of his music. He still remains grounded in soul-jazz -- any guitar-organ combo is bound to have soul-jazz roots -- but he pushes the music toward adventurous hard bop, often with rewarding results".[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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