Anti-discrete space
From Encyclopedia of Mathematics
Revision as of 16:52, 20 June 2016 by Richard Pinch (talk | contribs) (Expand, cite Steen and Seebach)
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=53671
Anti-discrete space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anti-discrete_space&oldid=53671
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