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In mathematics, in the field of topology, a perfect set is a closed set with no isolated points and a perfect space is any topological space with no isolated points. In such spaces, every point can be approximated arbitrarily well by other points: given any point and any topological neighborhood of the point, there is another point within the neighborhood. The term ''perfect space'' is also used, incompatibly, to refer to other properties of a topological space, such as being a Gδ space. Context is required to determine which meaning is intended. In this article, a space which is not perfect will be referred to as imperfect. ==Examples and nonexamples== The real line is a connected perfect space, while the Cantor space 2ω and Baire space ωω are perfect, totally disconnected zero-dimensional spaces. Any nonempty set admits an imperfect topology: the discrete topology. Any set with more than one point admits a perfect topology: the indiscrete topology. 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「Perfect set」の詳細全文を読む スポンサード リンク
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