  We present an easy proof that $p$--Hardy's inequality implies uniform
$p$--fatness of the boundary when $p=n$. The proof works also in metric space
setting and demonstrates the self--improving phenomenon of the $p$--fatness. We
also explore the relationship between $p$-fatness, $p$-Hardy inequality, and
the uniform perfectness for all $p\ge 1$, and demonstrate that in the Ahlfors
$Q$-regular metric measure space setting with $p=Q$, these three properties are
equivalent.
