  Given a continuum $X$ and an element $x \in X$, $\pi(x)$ is the smallest set
that contains $x$ and does not block singletons, and $B(x)$ is the set of all
elements blocked by ${x}$. We prove that for each $x \in X$, $B(x)$ is
connected, $B(x) \subset \pi(x)$, and that if $B(x)$ is closed, then
$B(x)=\pi(x)$. Among other results, we prove that if $X$ is a Kelley continuum
and $\pi(x)$ is proper, then $B(x)=\pi(x)$. Finally, we prove that for a
certain class of dendroids, the family of minima non-blockers coincides with
the family of connected non-blockers.
