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- In topology, a cut-point is a point of a connected space such that its removal causes the resulting space to be disconnected. If removal of a point doesn't result in disconnected spaces, this point is called a non-cut point. For example, every point of a line is a cut-point, while no point of a circle is a cut-point. Cut-points are useful to determine whether two connected spaces are homeomorphic by counting the number of cut-points in each space. If two spaces have different number of cut-points, they are not homeomorphic. A classic example is using cut-points to show that lines and circles are not homeomorphic. Cut-points are also useful in the characterization of topological continua, a class of spaces which combine the properties of compactness and connectedness and include many familiar spaces such as the unit interval, the circle, and the torus. (en)
- 일반위상수학에서 절단점(切斷點, 영어: cut-point)은 연결 공간을 연결되지 않은 둘 이상의 부분들로 분리하는 점이다. (ko)
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- 일반위상수학에서 절단점(切斷點, 영어: cut-point)은 연결 공간을 연결되지 않은 둘 이상의 부분들로 분리하는 점이다. (ko)
- In topology, a cut-point is a point of a connected space such that its removal causes the resulting space to be disconnected. If removal of a point doesn't result in disconnected spaces, this point is called a non-cut point. For example, every point of a line is a cut-point, while no point of a circle is a cut-point. Cut-points are also useful in the characterization of topological continua, a class of spaces which combine the properties of compactness and connectedness and include many familiar spaces such as the unit interval, the circle, and the torus. (en)
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