  In this note, we shall generalize the notion of a $P$-space to proximity
spaces and investigate the basic properties of these proximities. We therefore
define a $P_{\aleph_{1}}$-proximity to be a proximity where if $A_{n}\prec B$
for all $n\in\mathbb{N}$, then $\bigcup_{n}A_{n}\prec B$. It turns out that the
class of $P_{\aleph_{1}}$-proximities is equivalent to the class of
$\sigma$-algebras. Furthermore, the $P_{\aleph_{1}}$-proximity coreflection of
a proximity space is the $\sigma$-algebra of proximally Baire sets.
