View source for Dispersive space

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''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 [[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]].

====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>