Discrete two-point space

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In topology, a branch of mathematics, a discrete two-point space is the simplest example of a totally disconnected discrete space. The points can be denoted by the symbols 0 and 1.

Any disconnected space has a continuous mapping onto the discrete two-point space. Conversely if a continuous mapping to the discrete two-point space exists from a topological space, the space is disconnected.[1]


  1. ^ George F. Simmons (1968). Introduction to Topology and Modern Analysis. McGraw–Hill Book Company. p. 144.