# Difference between revisions of "Anti-discrete space"

From Encyclopedia of Mathematics

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+ | ''indiscrete space'' | ||

+ | A [[topological space]] in which only the empty set and the entire space are open. | ||

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

====Comments==== | ====Comments==== | ||

− | Other frequently occurring names for this topological space are indiscrete space and trivial topological space. | + | 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. |

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+ | ====References==== | ||

+ | <table> | ||

+ | <TR><TD valign="top">[a1]</TD> <TD valign="top"> Steen, Lynn Arthur; Seebach, J.Arthur jun. ''Counterexamples in topology'' (2nd ed.) Springer (1978) ISBN 0-387-90312-7 {{ZBL|0386.54001}}</TD></TR> | ||

+ | </table> |

## Latest revision as of 16:52, 20 June 2016

*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://encyclopediaofmath.org/index.php?title=Anti-discrete_space&oldid=32068

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