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Groups are also applied in many other mathematical areas. Mathematical objects are often examined by associating groups to them and studying the properties of the corresponding groups. For example, Henri Poincare founded what is now called algebraic topology by introducing the fundamental group. By means of this connection, topological properties such as proximity and continuity translate into properties of groups.i["] For example, elements of the fundamental group are represented by loops. The second image at the right shows some loops in a plane minus a point. The blue loop is considered null-homotopic (and thus irrelevant), because it can be continuously shrunk to a point. The presence of the hole prevents the orange loop from being shrunk to a point. The fundamental group of the plane with a point deleted turns out to be infinite cyclic, generated by the orange loop (or any other loop winding once around the hole). This way, the fundamental group detects the hole.
What did Henri Poincare introduce when he established algebraic topology?
A: the fundamental group

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Unlike the American GPS, Russian GLONASS, and European Galileo systems, which use medium Earth orbit satellites, BeiDou-1 uses satellites in geostationary orbit. This means that the system does not require a large constellation of satellites, but it also limits the coverage to areas on Earth where the satellites are visible. The area that can be serviced is from longitude 70E to 140E and from latitude 5N to 55N. A frequency of the system is 2491.75 MHz.
What type of satellites does the American GPS system use?
A: medium Earth orbit satellites

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In the past, the floor exercise event was executed on the bare floor or mats such as wrestling mats. Today, the floor event occurs on a carpeted 12m 12m square, usually consisting of hard foam over a layer of plywood, which is supported by springs or foam blocks generally called a "spring" floor. This provides a firm surface that provides extra bounce or spring when compressed, allowing gymnasts to achieve greater height and a softer landing after the composed skill. Gymnasts perform a choreographed routine up to 90 seconds in the floor exercise event; Depending on the level, they may choose their own, or, if known as a "compulsory gymnast," default music must be played. In some gymnastic associations such as United States Association of Gymnastic Clubs (USAIGC), gymnasts are allowed to have vocals in their music but at USA Gymnastics competitions a large deduction is taken from the score for having vocals in the music. The routine should consist of tumbling lines, series of jumps, leaps, dance elements, acrobatic skills, and turns, or piviots, on one foot. A gymnast can perform up to four tumbling lines that usually includes at least one flight element without hand support. Each level of gymnastics requires the athlete to perform a different number of tumbling passes. In level 7 in the United States, a gymnast is required to do 23, and in levels 810, at least 34 tumbling passes are required.
What kind of surface is banned from the Olympics?
A: unanswerable

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West is among the most critically acclaimed artists of the twenty-first century, receiving praise from music critics, fans, fellow musicians, artists, and wider cultural figures for his work. AllMusic editor Jason Birchmeier writes of his impact, "As his career progressed throughout the early 21st century, West shattered certain stereotypes about rappers, becoming a superstar on his own terms without adapting his appearance, his rhetoric, or his music to fit any one musical mold." Jon Caramanic of The New York Times said that West has been "a frequent lightning rod for controversy, a bombastic figure who can count rankling two presidents among his achievements, along with being a reliably dyspeptic presence at award shows (when he attends them)." Village Voice Media senior editor Ben Westhoff dubbed him the greatest hip hop artist of all time, writing that "he's made the best albums and changed the game the most, and his music is the most likely to endure," while Complex called him the 21st century's "most important artist of any art form, of any genre." The Guardian has compared West to David Bowie, arguing that "there is nobody else who can sell as many records as West does (30m-odd album sales and counting) while remaining so resolutely experimental and capable of stirring things up culturally and politically."
Who said Kanye West was the greatest hip hop artist of all time?
A:
Ben Westhoff