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Taipei (), officially Taipei City, is the capital and a special municipality of Taiwan (officially the Republic of China, ROC). Located in northern Taiwan, Taipei City is an enclave of the municipality of New Taipei City that sits about 25 km (16 mi) southwest of the northern port city of Keelung. Most of the city lies on the Taipei Basin, an ancient lakebed. The basin is bounded by the relatively narrow valleys of the Keelung and Xindian rivers, which join to form the Tamsui River along the city's western border.The city proper is home to an estimated population of 2,646,204 (2019), forming the core part of the Taipei–Keelung metropolitan area, which includes the nearby cities of New Taipei and Keelung with a population of 7,047,559, the 40th most-populous urban area in the world—roughly one-third of Taiwanese citizens live in the metro district. The name "Taipei" can refer either to the whole metropolitan area or the city proper.
Taipei is the political, economic, educational, and cultural center of Taiwan and one of the major hubs in East Asia. Considered to be a global city and rated as an Alpha - City by GaWC, Taipei is part of a major high-tech industrial area.
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Manhattan (), often referred to by residents of the New York City area as the City, is the most densely populated of the five boroughs of New York City, and coextensive with the County of New York, one of the original counties of the U.S. state of New York. Manhattan serves as the city's economic and administrative center, cultural identifier, and historical birthplace. The borough consists mostly of Manhattan Island, bounded by the Hudson, East, and Harlem rivers; as well as several small adjacent islands. Manhattan additionally contains Marble Hill, a small neighborhood now on the U.S. mainland, separated from the rest of Manhattan by the Harlem Ship Canal and later connected using landfill to the Bronx. Manhattan Island is divided into three informally bounded components, each aligned with the borough's long axis: Lower, Midtown, and Upper Manhattan.
Manhattan has been described as the cultural, financial, media, and entertainment capital of the world, and the borough hosts the United Nations Headquarters. Anchored by Wall Street in the Financial District of Lower Manhattan, New York City has been called both the most economically powerful city and the leading financial center of the world, and Manhattan is home to the world's two largest stock exchanges by total market capitalization: the New York Stock Exchange and NASDAQ. Many multinational media conglomerates are based in Manhattan, and the borough has been the setting for numerous books, films, and television shows. Manhattan real estate has since become among the most expensive in the world, with the value of Manhattan Island, including real estate, estimated to exceed US$3 trillion in 2013; median residential property sale prices in Manhattan approximated US$1,600 per square foot ($17,000/m2) as of 2018, with Fifth Avenue in Midtown Manhattan commanding the highest retail rents in the world, at US$3,000 per square foot ($32,000/m2) per year in 2017.Manhattan traces its origins to a trading post founded by colonists from the Dutch Republic in 1624 on Lower Manhattan; the post was named New Amsterdam in 1626. Manhattan is historically documented to have been purchased by Dutch colonists from Native Americans in 1626 for 60 guilders, which equals roughly $1059 in current terms. The territory and its surroundings came under English control in 1664 and were renamed New York after King Charles II of England granted the lands to his brother, the Duke of York.