The
M
M
-ideals in
B
(
C
0
(
Ω
)
)
B({C_0}(\Omega ))
, the space of continuous linear operators on
C
0
(
Ω
)
{C_0}(\Omega )
, are determined where
Ω
\Omega
is a locally compact Hausdorff countably paracompact space. A one-to-one correspondence between
M
M
-ideals in
B
(
C
0
(
Ω
)
)
B({C_0}(\Omega ))
, open subsets of the Stone-Čech compactification of
Ω
\Omega
, and lower semicontinuous Hermitian projections in
B
(
C
0
(
Ω
)
)
∗
∗
B{({C_0}(\Omega ))^{\ast \ast }}
is established.