<s>
An	O
ordered	O
vector	O
space	O
is	O
called	O
order	B-Algorithm
complete	I-Algorithm
,	O
Dedekind	O
complete	O
,	O
a	O
complete	O
vector	B-Algorithm
lattice	I-Algorithm
,	O
or	O
a	O
complete	O
Riesz	B-Algorithm
space	I-Algorithm
,	O
if	O
it	O
is	O
order	B-Algorithm
complete	I-Algorithm
as	O
a	O
subset	O
of	O
itself	O
,	O
in	O
which	O
case	O
it	O
is	O
necessarily	O
a	O
vector	B-Algorithm
lattice	I-Algorithm
.	O
</s>
<s>
An	O
ordered	O
vector	O
space	O
is	O
said	O
to	O
be	O
countably	O
order	B-Algorithm
complete	I-Algorithm
if	O
each	O
countable	O
subset	O
that	O
is	O
bounded	O
above	O
has	O
a	O
supremum	O
.	O
</s>
<s>
Being	O
an	O
order	B-Algorithm
complete	I-Algorithm
vector	O
space	O
is	O
an	O
important	O
property	O
that	O
is	O
used	O
frequently	O
in	O
the	O
theory	O
of	O
topological	B-Algorithm
vector	I-Algorithm
lattices	I-Algorithm
.	O
</s>
<s>
The	O
order	B-Algorithm
dual	I-Algorithm
of	O
a	O
vector	B-Algorithm
lattice	I-Algorithm
is	O
an	O
order	B-Algorithm
complete	I-Algorithm
vector	B-Algorithm
lattice	I-Algorithm
under	O
its	O
canonical	O
ordering	O
.	O
</s>
<s>
If	O
is	O
a	O
locally	B-Algorithm
convex	I-Algorithm
topological	B-Algorithm
vector	I-Algorithm
lattice	I-Algorithm
then	O
the	O
strong	O
dual	O
is	O
an	O
order	B-Algorithm
complete	I-Algorithm
locally	B-Algorithm
convex	I-Algorithm
topological	B-Algorithm
vector	I-Algorithm
lattice	I-Algorithm
under	O
its	O
canonical	O
order	O
.	O
</s>
<s>
Every	O
reflexive	O
locally	B-Algorithm
convex	I-Algorithm
topological	B-Algorithm
vector	I-Algorithm
lattice	I-Algorithm
is	O
order	B-Algorithm
complete	I-Algorithm
and	O
a	O
complete	O
TVS	O
.	O
</s>
