  We present simple conditions for Bayesian consistency in the supremum metric.
The key to the technique is a triangle inequality which allows us to explicitly
use weak convergence, a consequence of the standard Kullback--Leibler support
condition for the prior. A further condition is to ensure that smoothed
versions of densities are not too far from the original density, thus dealing
with densities which could track the data too closely. A key result of the
paper is that we demonstrate supremum consistency using weaker conditions
compared to those currently used to secure $\mathbb{L}_1$ consistency.
