Difference between revisions of "Dispersive space"
From Encyclopedia of Mathematics
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''hereditarily disconnected space'' | ''hereditarily disconnected space'' | ||
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====Comments==== | ====Comments==== | ||
| − | 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 $x\neq y$ 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 [[ | + | See also [[Totally-disconnected space]]. |
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> K. Kuratowski, "Topology" , '''1–2''' , Acad. Press (1966–1968) (Translated from French)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian)</TD></TR></table> | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> K. Kuratowski, "Topology" , '''1–2''' , Acad. Press (1966–1968) (Translated from French)</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) (Translated from Russian)</TD></TR> | ||
| + | </table> | ||
Latest revision as of 18:11, 20 December 2014
2020 Mathematics Subject Classification: Primary: 54D05 [MSN][ZBL]
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 $x\neq y$ 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=30591
Dispersive space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dispersive_space&oldid=30591
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