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
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Barile, Margherita. "Totally Disconnected Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TotallyDisconnectedSpace.html