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Difference between revisions of "Anti-discrete space"

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A topological space in which only the empty set and the entire space are open.
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''indiscrete space''
  
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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====
 
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Other frequently occurring names for this topological space are indiscrete space and trivial topological space.
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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====
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<table>
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<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>
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</table>

Latest revision as of 14:03, 8 April 2023


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=13558
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
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