Anti-discrete space

indiscrete space

A topological space in which only the empty set and the entire space are open.

Any function from a topological space to an anti-discrete space is continuous.

Comments

Other frequently occurring names for this topological space are indiscrete space and trivial topological space, although the latter term can also refer specifically to a space with only one point.

References

[a1]	Steen, Lynn Arthur; Seebach, J.Arthur jun. Counterexamples in topology (2nd ed.) Springer (1978) ISBN 0-387-90312-7 Zbl 0386.54001