Theorem
The set of rational numberswith the Euclidean topology is totally disconnected.
Proof
Letand let
An irrational numberexists satisfying
Define setsand
by
and
so
is totally disconnected.
Theorem
The set of rational numberswith the Euclidean topology is totally disconnected.
Proof
Letand let
An irrational numberexists satisfying
Define setsand
by
and
so
is totally disconnected.