Dispersive space
From Encyclopedia of Mathematics
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 
in 
there is a closed and open set 
such that 
and 
. 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