A compact set must be bounded and closed. Compact set refers to a kind of special point set in topological space, and any open cover of them has finite sub-covers. In a sense, a compact set is similar to a closed set.

Set, for short, is a basic concept in mathematics and the main research object of set theory.

The basic theory of set theory was founded in19th century. The simplest statement about set is the definition in naive set theory (the most primitive set theory), that is, set is "a certain pile of things" and the "things" in set are called elements. A modern set is usually defined as a whole consisting of one or more definite elements.

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Set has unparalleled special importance in the field of mathematics. The foundation of set theory was laid by German mathematician Cantor in the 1970s of 19. After the efforts of a large number of scientists for half a century, it established its basic position in the modern mathematical theory system in the 1920s. It can be said that the achievements of all branches of modern mathematics are almost based on strict set theory.

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