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.
Properties
Any disconnected space has a continuous mapping which is not constant onto the discrete two-point space. Conversely if a nonconstant continuous mapping to the discrete two-point space exists from a topological space, the space is disconnected.1
References
References
- George F. Simmons (1968). Introduction to Topology and Modern Analysis. McGraw–Hill Book Company. p. 144.