<s>
The	O
Mackey	B-Algorithm
–	I-Algorithm
Arens	I-Algorithm
theorem	I-Algorithm
is	O
an	O
important	O
theorem	O
in	O
functional	B-Application
analysis	I-Application
that	O
characterizes	O
those	O
locally	B-Algorithm
convex	I-Algorithm
vector	B-Architecture
topologies	I-Architecture
that	O
have	O
some	O
given	O
space	O
of	O
linear	B-Algorithm
functionals	I-Algorithm
as	O
their	O
continuous	O
dual	O
space	O
.	O
</s>
<s>
According	O
to	O
Narici	O
(	O
2011	O
)	O
,	O
this	O
profound	O
result	O
is	O
central	O
to	O
duality	B-Algorithm
theory	I-Algorithm
;	O
a	O
theory	O
that	O
is	O
"	O
the	O
central	O
part	O
of	O
the	O
modern	O
theory	O
of	O
topological	O
vector	O
spaces.	O
"	O
</s>
<s>
If	O
is	O
any	O
other	O
locally	B-Algorithm
convex	I-Algorithm
Hausdorff	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
topology	O
on	O
,	O
then	O
we	O
say	O
that	O
is	O
compatible	O
with	O
duality	O
between	O
and	O
if	O
when	O
is	O
equipped	O
with	O
,	O
then	O
it	O
has	O
as	O
its	O
continuous	O
dual	O
space	O
.	O
</s>
<s>
If	O
we	O
give	O
the	O
weak	O
topology	O
then	O
is	O
a	O
Hausdorff	O
locally	B-Algorithm
convex	I-Algorithm
topological	I-Algorithm
vector	I-Algorithm
space	I-Algorithm
(	O
TVS	O
)	O
and	O
is	O
compatible	O
with	O
duality	O
between	O
and	O
(	O
i.e.	O
</s>
<s>
We	O
can	O
now	O
ask	O
the	O
question	O
:	O
what	O
are	O
all	O
of	O
the	O
locally	B-Algorithm
convex	I-Algorithm
Hausdorff	O
TVS	O
topologies	O
that	O
we	O
can	O
place	O
on	O
that	O
are	O
compatible	O
with	O
duality	O
between	O
and	O
?	O
</s>
<s>
The	O
answer	O
to	O
this	O
question	O
is	O
called	O
the	O
Mackey	B-Algorithm
–	I-Algorithm
Arens	I-Algorithm
theorem	I-Algorithm
.	O
</s>
