# Anti-discrete space

From Encyclopedia of Mathematics

*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 |

**How to Cite This Entry:**

Anti-discrete space.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Anti-discrete_space&oldid=38994

This article was adapted from an original article by A.A. Mal'tsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article