Difference between revisions of "Dispersive space"
From Encyclopedia of Mathematics
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| − | Some authors call spaces as above totally disconnected. However, a space is commonly called totally disconnected if for all | + | Some authors call spaces as above totally disconnected. However, a space is commonly called totally disconnected if for all $x\notin y$ in $X$ there is a [[Open-closed set|closed and open set]] $C$ such that $x\in C$ and $y\notin C$. A closed and open set is also called a clopen set. |
See also [[Totally-disconnected space|Totally-disconnected space]]. | See also [[Totally-disconnected space|Totally-disconnected space]]. | ||
Revision as of 15:27, 6 August 2014
hereditarily disconnected space
A topological space which contains no connected sets with more than one point.
Comments
Some authors call spaces as above totally disconnected. However, a space is commonly called totally disconnected if for all $x\notin y$ in $X$ there is a closed and open set $C$ such that $x\in C$ and $y\notin C$. A closed and open set is also called a clopen set.
See also Totally-disconnected space.
References
| [a1] | K. Kuratowski, "Topology" , 1–2 , Acad. Press (1966–1968) (Translated from French) |
| [a2] | A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian) |
How to Cite This Entry:
Dispersive space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dispersive_space&oldid=32744
Dispersive space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dispersive_space&oldid=32744
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