A totally disconnected space is a space in which all subsets with more than one element are disconnected. In particular, if it has more than one element, it is a disconnected
set, and the singleton sets are its connected components. Every discrete space is
disconnected, and so are the Cantor set and the set of rationals with respect to
the relative topology induced by the Euclidean topology of 
.
Totally Disconnected Space
This entry contributed by Margherita Barile
Explore with Wolfram|Alpha
Cite this as:
Barile, Margherita. "Totally Disconnected Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TotallyDisconnectedSpace.html