Difference between revisions of "Anti-discrete space"
From Encyclopedia of Mathematics
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A [[topological space]] in which only the empty set and the entire space are open. | 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==== | ====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. | 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> | ||
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=37316
Anti-discrete space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Anti-discrete_space&oldid=37316
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