Indiscrete space
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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.