Theorem
A space
containinga connected dense subspace is connected.
Proof
Let
bea connected dense subspace of
sothat
If
isa connected subset of
and
then
isconnected.
Sinceisdense in
andsinceisconnected, so is
Call Us 07766496223
Theorem
A spacecontaininga connected dense subspace is connected.
Proof
Letbea connected dense subspace ofsothat
Ifisa connected subset ofandthenisconnected.
Sinceisdense inandsinceisconnected, so is