Cut-point

The "neck" of this eight-like figure is a cut-point.

In topology, a cut-point is a point of a connected space such that its removal causes the resulting space to be disconnected. 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 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.

Definition

A cut-point of a connected T1 topological space X, is a point p in X such that X - {p} is not connected. A point which is not a cut-point is called a noncut-point.

Properties

References


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