  The existence, established over the past number of years and supporting
earlier work of Ori [14], of physically relevant black hole spacetimes that
admit $C^0$ metric extensions beyond the future Cauchy horizon, while being
$C^2$-inextendible, has focused attention on fundamental issues concerning the
strong cosmic censorship conjecture. These issues were recently discussed in
the work of Jan Sbierski [17], in which he established the (nonobvious) fact
that the Schwarschild solution in global Kruskal-Szekeres coordinates is
$C^0$-inextendible. In this paper we review aspects of Sbierski's methodology
in a general context, and use similar techniques, along with some new
observations, to consider the $C^0$-inextendibility of open FLRW cosmological
models. We find that a certain special class of open FLRW spacetimes, which we
have dubbed `Milne-like,' actually admit $C^0$ extensions through the big bang.
For spacetimes that are not Milne-like, we prove some inextendibility results
within the class of spherically symmetric spacetimes.
