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Recall a space is totally disconnected if the only connected subsets are singletons (one-point subsets). Is a totally disconnected space, Hausdorff?
I think it is true since if $a $ and $b $ are two distinct points, they can be separated two disjoint open sets, since the main space is totally disconnected (see Theorem at < http://www.emathzone.com/tutorials/general-topology/totally-disconnected-space.html >).
Is this argument true?