In this paper we use the techniques of analytic topology to establish a conjecture of A. H. Stone: A perfectly normal, locally connected, connected space is multicoherent if and only if there exist four nonempty, closed and connected subsets
A
0
,
A
1
,
A
2
,
A
3
{A_0},{A_1},{A_2},{A_3}
of X such that
⋃
i
=
0
3
A
i
=
X
\bigcup \nolimits _{i = 0}^3 {{A_i} = X}
and the nerve of
{
A
0
,
A
1
,
A
2
,
A
3
}
\{ {A_0},{A_1},{A_2},{A_3}\}
forms a closed 4-gon, i.e.
A
i
{A_i}
meets
A
i
+
1
{A_{i + 1}}
and
A
i
−
1
{A_{i - 1}}
and no others (the suffices being taken
mod
4
\bmod \; 4
).