<s>
In	O
mathematics	O
,	O
specifically	O
in	O
order	O
theory	O
and	O
functional	B-Application
analysis	I-Application
,	O
an	O
abstract	B-Algorithm
m-space	I-Algorithm
or	O
an	O
AM-space	B-Algorithm
is	O
a	O
Banach	O
lattice	O
whose	O
norm	O
satisfies	O
for	O
all	O
x	O
and	O
y	O
in	O
the	O
positive	O
cone	O
of	O
X	O
.	O
</s>
<s>
We	O
say	O
that	O
an	O
AM-space	B-Algorithm
X	O
is	O
an	O
AM-space	B-Algorithm
with	O
unit	O
if	O
in	O
addition	O
there	O
exists	O
some	O
in	O
X	O
such	O
that	O
the	O
interval	O
is	O
equal	O
to	O
the	O
unit	O
ball	O
of	O
X	O
;	O
</s>
<s>
The	O
strong	O
dual	O
of	O
an	O
AL-space	B-Algorithm
is	O
an	O
AM-space	B-Algorithm
with	O
unit	O
.	O
</s>
<s>
If	O
X	O
is	O
an	O
Archimedean	B-Algorithm
ordered	I-Algorithm
vector	B-Algorithm
lattice	I-Algorithm
,	O
u	O
is	O
an	O
order	O
unit	O
of	O
X	O
,	O
and	O
pu	O
is	O
the	O
Minkowski	O
functional	O
of	O
then	O
the	O
complete	O
of	O
the	O
semi-normed	O
space	O
(	O
X	O
,	O
pu	O
)	O
is	O
an	O
AM-space	B-Algorithm
with	O
unit	O
u	O
.	O
</s>
<s>
Every	O
AM-space	B-Algorithm
is	O
isomorphic	O
(	O
as	O
a	O
Banach	O
lattice	O
)	O
with	O
some	O
closed	O
vector	O
sublattice	O
of	O
some	O
suitable	O
.	O
</s>
<s>
The	O
strong	O
dual	O
of	O
an	O
AM-space	B-Algorithm
with	O
unit	O
is	O
an	O
AL-space	B-Algorithm
.	O
</s>
<s>
If	O
X	O
≠	O
{	O
0	O
}	O
is	O
an	O
AM-space	B-Algorithm
with	O
unit	O
then	O
the	O
set	O
K	O
of	O
all	O
extreme	O
points	O
of	O
the	O
positive	O
face	O
of	O
the	O
dual	O
unit	O
ball	O
is	O
a	O
non-empty	O
and	O
weakly	O
compact	O
(	O
i.e.	O
</s>
