Namespaces
Variants
Actions

Difference between revisions of "Anti-discrete space"

From Encyclopedia of Mathematics
Jump to: navigation, search
(Expand, cite Steen and Seebach)
(2 intermediate revisions by 2 users not shown)
Line 1: Line 1:
A topological space in which only the empty set and the entire space are open.
+
{{TEX|done}}
  
 +
''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====
 
====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.
 +
 
 +
====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=29407
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