<s>
The	O
space	O
of	O
bounded	O
real-valued	O
maps	O
on	O
a	O
set	O
with	O
the	O
pointwise	O
order	O
is	O
Archimedean	B-Algorithm
ordered	I-Algorithm
with	O
an	O
order	O
unit	O
(	O
that	O
is	O
,	O
the	O
function	O
that	O
is	O
identically	O
on	O
)	O
.	O
</s>
<s>
Every	O
order	B-Algorithm
complete	I-Algorithm
vector	B-Algorithm
lattice	I-Algorithm
is	O
Archimedean	B-Algorithm
ordered	I-Algorithm
.	O
</s>
<s>
A	O
finite-dimensional	O
vector	B-Algorithm
lattice	I-Algorithm
of	O
dimension	O
is	O
Archimedean	B-Algorithm
ordered	I-Algorithm
if	O
and	O
only	O
if	O
it	O
is	O
isomorphic	O
to	O
with	O
its	O
canonical	O
order	O
.	O
</s>
<s>
However	O
,	O
a	O
totally	O
ordered	O
vector	O
order	O
of	O
dimension	O
can	O
not	O
be	O
Archimedean	B-Algorithm
ordered	I-Algorithm
.	O
</s>
