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Topological group

In mathematics, a topological group is a group G together with a topology on G such that both the group's binary operation and the function mapping group elements to their respective inverses are continuous functions with respect to the topology. A topological group is a mathematical object with both an algebraic structure and a topological structure. Thus, one may perform algebraic operations, because of the group structure, one may talk about continuous functions, because of the topology. Topological groups, along with continuous group actions, are used to study continuous symmetries, which have many applications, for example, in physics. A topological group, G, is a topological space, a group such that the group operations of product: G × G → G: ↦ x y and taking inverses: G → G: x ↦ x − 1 are continuous. Here G × G is viewed as a topological space with the product topology. So the product is continuous if for all open U ⊆ G such that x y ∈ U, there exists open V × W ⊆ G × G with ∈ V × W and V ⋅ W:= ⊆ U, taking inverses is continuous if for all open U ⊆ G with x − 1 ∈ U, there exists an open V ⊆ G with x ∈ V, such that V − 1:= ⊆ U.

Although not part of this definition, many authors require. The reasons, some equivalent conditions, are discussed below. In any case, any topological group can be made Hausdorff by taking an appropriate canonical quotient. In the language of category theory, topological groups can be defined concisely as group objects in the category of topological spaces, in the same way that ordinary groups are group objects in the category of sets. Note that the axioms are given in terms of the maps, hence are categorical definitions. A homomorphism of topological groups means a continuous group homomorphism G → H. An isomorphism of topological groups is a group isomorphism, a homeomorphism of the underlying topological spaces; this is stronger than requiring a continuous group isomorphism—the inverse must be continuous. There are examples of topological groups that are isomorphic as ordinary groups but not as topological groups. Indeed, any non-discrete topological group is a topological group when considered with the discrete topology.

The underlying groups are the same. Topological groups, together with their homomorphisms, form a category; every group can be trivially made into a topological group by considering it with the discrete topology. In this sense, the theory of topological groups subsumes that of ordinary groups; the real numbers, R with the usual topology form a topological group under addition. Euclidean n-space Rn is a topological group under addition, more every topological vector space forms an topological group; some other examples of abelian topological groups are the circle group S1, or the torus n for any natural number n. The classical groups are important examples of non-abelian topological groups. For instance, the general linear group GL of all invertible n-by-n matrices with real entries can be viewed as a topological group with the topology defined by viewing GL as a subspace of Euclidean space Rn×n. Another classical group is the orthogonal group O, the group of all linear maps from Rn to itself that preserve the length of all vectors.

The orthogonal group is compact as a topological space. Much of Euclidean geometry can be viewed as studying the structure of the orthogonal group, or the related group O ⋉ Rn of isometries of Rn; the groups mentioned so far are all Lie groups, meaning that they are smooth manifolds in such a way that the group operations are smooth, not just continuous. Lie groups are the best-understood topological groups.

Igor Siqueira Pessanha

Igor Siqueira Pessanha or Igor is a Brazilian footballer who plays as a striker for Santo André in Brazil. Igor moved to Campeonato Brasileiro Série C club, Adap Galo Maringá from Corinthians for the 2007 season, he was transferred to Sevilla on 1 August 2007 on a five-year contract. He participated in the 2005 FIFA World U-17 Cup for Brazil, played the whole final where they lost 3-0 to Mexico, he was joint runner-up to the golden boot, bagging four goals in the tournament. He has played for various levels at the national set-up from U-15 to U-17, scoring a total of 37 goals in 50 games. Stats at ForaDeJogo esportes

Charles Holder

Charles Garrett Holder was a politician from Alberta, Canada. He served in the Legislative Assembly of Alberta from 1935 to 1940 and from 1944 to 1948 as a member of the Social Credit caucus. Holder ran for a seat to the Alberta Legislature for the first time in the 1935 general election, as a Social Credit candidate in the electoral district of St. Albert, he defeated incumbent Omer St. Germain to pick up the seat for his party. Holder ran for a second term in the 1940 general election, he was defeated by independent candidate Lionel Tellier on the fourth count. Holder was nominated to run for Social Credit again at a convention held in Morinville on February 9, 1944, he ran in the general election won on the second vote count. He retired from the assembly at dissolution in 1948. Legislative Assembly of Alberta Members Listing

Lancelot Link, Secret Chimp

Lancelot Link, Secret Chimp is an American action/adventure comedy series that aired on ABC from September 12, 1970 to January 2, 1971. The Saturday morning live-action film series featured a cast of chimpanzees given apparent speaking roles by overdubbing with human voices. Lancelot Link, Secret Chimp had a "seven-figure budget" with location filming and costumes, the laborious staging and training of the animals; the filmmakers made the most of the budget, staging multiple episodes with the same settings and wardrobe reusing the more elaborate chase footage. Lance Link drove a 1970 Datsun Sports 2000 while villain Baron Von Butcher used a late-'50s Rolls-Royce Silver Cloud; the primates themselves rode. Two of the three producers/creators were Stan Burns and Mike Marmer, former writers for Get Smart! Both resigned from their jobs as head writers on The Carol Burnett Show to work on Lancelot Link, Secret Chimp. According to The Believer, "to make the dialogue fit the chimps’ lip action and Marmer went to ridiculous lengths.

Voiceovers were ad-libbed on the set, giving birth to beautifully absurd moments of the chimps breaking into songs at the end of sentences or spontaneously reciting Mother Goose rhymes just so it would look right." Owing considerable lineage to Get Smart, the plot was always played for laughs and featured Lancelot Link and his female colleague, "Mata Hairi," whose own name in turn was a play on Mata Hari, in secret agent and spy satires. Link worked for A. P. E; the Agency to Prevent Evil, in an ongoing conflict with the evil organization C. H. U. M. P; the Criminal Headquarters for the Underworld's Master Plan. APE's chief Darwin gave Link and Hairi their orders as part of his "theory," a play on the Charles Darwin theory of evolution. CHUMP's monocled chief Baron von Butcher hatched the latest plan to endanger the world; the Baron's network of international fiends included his shifty chauffeur Creto, mad scientist Dr. Strangemind, imperious Dragon Woman, drowsy Wang Fu, singing sheikh Ali Assa Seen, the cultured Duchess.

One or more would appear in each episode. A regular weekly feature was chimp TV host "Ed Simian" introducing a musical number by an all-chimp band, "The Evolution Revolution." An album of these songs was released on the ABC/Dunhill record label. There were Lancelot Link comic books and other merchandise, including Halloween costumes. Another regular feature consisted of a short series of brief comedy sketches which showed a chimp sneezing causing a funny gag to happen. A curious feature of the apartment set which Lancelot Link and Mata Hairi used as their base was that the sofa had a secret entrance/exit, opened by lifting one of the cushions; the episodes were all narrated, by Malachi Throne. Lancelot Link - His surname is a reference to'The Missing Link' Mata Hairi - Her name was a take-off on Mata Hari. Commander Darwin - Named after Charles Darwin. Bruce - Official A. P. E. Courier. Baron von Butcher - Modeled on Kopell's character of "Siegfried" in the television show Get Smart! Kopell is believed to have approached his voicings of the Baron as if Siegfried were the head of KAOS.

The Dragon Woman - Her name was a take-off on the Dragon Lady, a villainess in the Terry and the Pirates comic strip series. Creto - His name was a play on the word "cretin." A play on Kato, the Green Hornet's chauffeur and crime-fighting "sidekick". Wang Fu - His name was a play on Kung Fu; the Duchess Ali Assa Seen - His last name was meant to sound like "assassin." Dr. Strangemind - Name inspired by Dr. Strangelove. Marty Mandrill - Former songwriter for The Evolution Revolution turned C. H. U. M. P. Spy. Unnamed Orangutan - Appeared in cameos as a picturesque extra. Referred to by Lance as "that weirdo". Blackie - The drummer in The Evolution Revolution. Ed Simian - A parody of famous television MC Ed Sullivan. Parnelli Smith - An auto racing champ and supplier of cars to A. P. E, his name was a take-off on former Indy 500 champion Parnelli Jones. Bart Sparks - MC of the Miss Globe contest. Herman - C. H. U. M. P. Henchman; this all-chimp band, dressed in colorful hippie-style wigs and wardrobe, featured Lancelot Link on guitar and Mata Hairi on tambourine, with Blackie as "Bananas Marmoset" on the drums.

"SweetWater Gibbons" was credited for playing Farfisa organ, although the organ pictured in the clips was a Vox Continental organ. In the episode "The Evolution Revolution", it was established that the band's music was used to communicate coded messages for A. P. E. Agents; the songs were co-written and performed by Steve Hoffman, in the Bubblegum pop style in vogue. A Lancelot Link record album was released on ABC/Dunhill, as well as a single titled "Sha-La Love You", a song intended for The Grass Roots; some songs contained heavy guitar riffs. An Evolution Revolution song, "Wild Dreams, Jelly

Dixie Hollins High School

Dixie M. Hollins High School is a public secondary school located in St. Petersburg, Florida; the school was opened in 1959 as a vocational school for grades 10–12, but it has since expanded to offer 9th grade education. The current population of the school is just under 1,800 students, its graphic arts program, known as the Academy of Entertainment Arts, is designated as a center of excellence. Dixie Hollins offers a program in the culinary arts, designated as a center of excellence; the school offers Cambridge/AICE curriculum, as well as a Junior Reserve Officers' Training Corps program. When Pinellas County separated from Hillsborough County and became its own entity in 1912, Dixie Maurice Hollins was appointed as Superintendent of Pinellas County Schools. Hollins promoted the rights of black students to have certified teachers, to attend a full school day, to attend school for more than just a few months per year; when Dixie Hollins High School opened its doors for the first time in the fall of 1959, it was first named Northwest High School.

The School Board decided to name the new high school after Dixie Hollins. Opening in 1959, Dixie Hollins High School was named after the first superintendent of Pinellas County Schools, the district in which the school is located, his family still operates one of the largest ranches in the state in Citrus County. He donated the land for both Madeira Beach Middle Schools. To this day his estate provides contributions to Dixie's music program. In 1971, the school became national news when the campus became embroiled in a community protest against racial integration through forced busing; the unrest had been building for several weeks. When the school decided to ban the use of the Confederate flag, community groups began picketing the school; the unrest broke out into violence on October 12, 1971. When Florida schools mandated kindergarten, Dixie Hollins High School incorporated 9th grade into its curriculum; the school underwent extensive renovations in 1992–1996, adding a two-story science wing, a new media center and cafeteria, an art building, a music building, upgrading the existing classrooms, the gymnasium, the vocational wing.

Official Pinellas County School Board website for Dixie M. Hollins High School

Jean Yu

Jean Yu is a Korean born fashion designer operating in New York City. She is a member of Council of Fashion Designers of America since 2007, was one of the top ten finalists for the CFDA/Vogue fashion fund in 2005. Yu was born in South Korea but her family moved to the United States and lived in California. Yu moved in New York to study at the Fashion Institute of Technology. While there, she produced her first dresses for a school project, she took the dress to shops in Soho, where they were sold. This inspired her to design a line of dresses that earned her the Innovator Design Award from Cotton Incorporated. After 9/11, Yu opened up her own boutique in December 2001. In 2005, she was named a finalist for the second annual Fashion Fund Award, created by the Council of Fashion Designers of America and Vogue Magazine. In 2007, she was a featured designer at the New York Fashion Exhibition at the Victoria & Albert Museum in London; as well, she was the recipient of Avenuel Designer award as Designer of the Year.

In 2014, she stepped away from lingerie and designed a wardrobe inspired by folk art for the show “Folk Couture: Fashion and Folk Art,” at the American Folk Art Museum. Jean Yu is known for her architectural approach and seamless technique, her lingerie have been described as "reinterpreting Old Hollywood glamour with a few innovative design twists."Her dresses have been featured in many fashion publications such as Vogue, Vanity Fair, The New York Times, W. Gwen Stefani was wearing her dress on the cover of the June 2004 edition of the American Vogue. Jean Yu's official site New York Times article