  We show that no exotic $\mathbb{R}^4$ admits a complete Riemannian metric
with uniformly positive isotropic curvature and with bounded geometry. This is
essentially a corollary of the main result in [Hu1], and was stated in [Hu2]
without proof. In the process of the proof we also show that the diffeomorphism
type of an infinite connected sum of some connected smooth $n$-manifolds
($n\geq 2$) according to a locally finite graph does not depend on the gluing
maps used.
