Indiscrete space

In topology, an indiscrete space is a topological space with the indiscrete topology, in which the only open subsets are the empty subset and the space itself.

Properties

• An indiscrete space is metrizable if and only if it has at most one point
• An indiscrete space is compact.
• An indiscrete space is connected.
• Every map from a topological space to an indiscrete space is continuous.

References

• Lynn Arthur Steen; J. Arthur Seebach jr (1978). Counterexamples in Topology. Berlin, New York: Springer-Verlag. ISBN 0-387-90312-7.