hereditarily disconnected space
A topological space which contains no connected sets with more than one point.
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.
|[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)|
Dispersive space. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Dispersive_space&oldid=35756