<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
Fréchet	O
lattice	O
is	O
a	O
topological	B-Algorithm
vector	I-Algorithm
lattice	I-Algorithm
that	O
is	O
also	O
a	O
Fréchet	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
Fréchet	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>
Every	O
Fréchet	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
set	O
of	O
all	O
weak	B-Algorithm
order	I-Algorithm
units	I-Algorithm
of	O
a	O
separable	O
Fréchet	B-Algorithm
lattice	I-Algorithm
is	O
a	O
dense	O
subset	O
of	O
its	O
positive	O
cone	O
.	O
</s>
<s>
Every	O
Banach	O
lattice	O
is	O
a	O
Fréchet	B-Algorithm
lattice	I-Algorithm
.	O
</s>
