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Closeness is a basic concept in topology and related areas in mathematics. Intuitively we say two sets are close if they are arbitrarily near to each other. The concept can be defined naturally in a metric space where a notion of distance between elements of the space is defined, but it can be generalized to topological spaces where we have no concrete way to measure distances. Note the difference between ''closeness'', which describes the relation between two sets, and ''closedness'', which describes a single set. The closure operator ''closes'' a given set by mapping it to a closed set which contains the original set and all points close to it. The concept of closeness is related to limit point. ==Definition== Given a metric space a point is called close or near to a set if :, where the distance between a point and a set is defined as :. Similarly a set is called close to a set if : where :. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Closeness (mathematics)」の詳細全文を読む スポンサード リンク
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