  This note consists of three unrelated remarks. First, we demonstrate how
roughly speaking $*$-homomorphisms between matrix stable $C^*$-algebras are
exactly the uniformly continuous $*$-preserving group homomorphisms between
their genral linear groups. Second, using the Cuntz picture in $KK$-theory we
bring morphisms in $KK$-theory represented by generators and relations to a
particular simple form. Third, we show that for an inverse semigroup its
associated groupoid is Hausdorff if and only if the inverse semigroup is
$E$-continuous.
