<s>
In	O
mathematics	O
,	O
specifically	O
in	O
order	O
theory	O
and	O
functional	B-Application
analysis	I-Application
,	O
a	O
normed	B-Algorithm
lattice	I-Algorithm
is	O
a	O
topological	B-Algorithm
vector	I-Algorithm
lattice	I-Algorithm
that	O
is	O
also	O
a	O
normed	O
space	O
whose	O
unit	O
ball	O
is	O
a	O
solid	B-Algorithm
set	I-Algorithm
.	O
</s>
<s>
Normed	B-Algorithm
lattices	I-Algorithm
are	O
important	O
in	O
the	O
theory	O
of	O
topological	B-Algorithm
vector	I-Algorithm
lattices	I-Algorithm
.	O
</s>
<s>
They	O
are	O
closely	O
related	O
to	O
Banach	O
vector	O
lattices	O
,	O
which	O
are	O
normed	B-Algorithm
vector	I-Algorithm
lattices	I-Algorithm
that	O
are	O
also	O
Banach	O
spaces	O
.	O
</s>
<s>
Every	O
normed	B-Algorithm
lattice	I-Algorithm
is	O
a	O
locally	B-Algorithm
convex	I-Algorithm
vector	I-Algorithm
lattice	I-Algorithm
.	O
</s>
<s>
The	O
strong	O
dual	O
of	O
a	O
normed	B-Algorithm
lattice	I-Algorithm
is	O
a	O
Banach	O
lattice	O
with	O
respect	O
to	O
the	O
dual	O
norm	O
and	O
canonical	O
order	O
.	O
</s>
<s>
If	O
it	O
is	O
also	O
a	O
Banach	O
space	O
then	O
its	O
continuous	O
dual	O
space	O
is	O
equal	O
to	O
its	O
order	B-Algorithm
dual	I-Algorithm
.	O
</s>
<s>
Every	O
Banach	O
lattice	O
is	O
a	O
normed	B-Algorithm
lattice	I-Algorithm
.	O
</s>
