Anti-discrete space

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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.


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.


[a1] Steen, Lynn Arthur; Seebach, J.Arthur jun. Counterexamples in topology (2nd ed.) Springer (1978) ISBN 0-387-90312-7 Zbl 0386.54001
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Anti-discrete space. Encyclopedia of Mathematics. URL:
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