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In general topology, a subset of a topological space is perfect if it is closed and has no isolated points. Equivalently: the set S {\displaystyle S} is perfect if S = S ′ {\displaystyle S=S'} , where S ′ {\displaystyle S'} denotes the set of all limit points of S {\displaystyle S} , also known as the derived set of S {\displaystyle S} .
Equivalently, a perfect set is a closed dense-in-itself set, or, put another way, a closed set with no isolated points. Perfect sets are particularly important in applications of the Baire category theorem. The Cantor–Bendixson theorem states that any Polish space can be written as the
Hence, every point in the Cantor set is an accumulation point (also called a cluster point or limit point) of the Cantor set, but none is an interior point. A closed set in which every point is an accumulation point is also called a perfect set in topology, while a closed subset of the interval with no interior points is nowhere dense in the ...
In the National Football League (NFL), the highest official passer rating that a player can achieve is 158.3, which is called a "perfect passer rating". [1] To qualify, during a single game a player must attempt at least 10 passes, have no interceptions, have a minimum completion percentage of 77.5%, have a minimum of 11.875% of their passes score touchdowns, and have a minimum of 12.5 yards ...
The Perfect Game: A Classic Collection of Facts, Figures, Stories and Characters from the Society for American Baseball Research (Taylor). ISBN 0-87833-815-2; Anderson, David W. (2000). More Than Merkle: A History of the Best and Most Exciting Baseball Season in Human History (Lincoln and London: University of Nebraska Press). ISBN 0-8032-1056-6
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A perfect game is the highest score possible in a game of bowling, achieved by scoring a strike with every throw. [1] In bowling games that use 10 pins, such as ten-pin bowling , candlepin bowling , and duckpin bowling , the highest possible score is 300, achieved by bowling 12 strikes in a row in a traditional single game: one strike in each ...