<s>
In	O
functional	B-Application
analysis	I-Application
and	O
related	O
areas	O
of	O
mathematics	O
,	O
the	O
Mackey	B-Algorithm
topology	I-Algorithm
,	O
named	O
after	O
George	O
Mackey	O
,	O
is	O
the	O
finest	O
topology	O
for	O
a	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
which	O
still	O
preserves	O
the	O
continuous	O
dual	O
.	O
</s>
<s>
In	O
other	O
words	O
the	O
Mackey	B-Algorithm
topology	I-Algorithm
does	O
not	O
make	O
linear	O
functions	O
continuous	O
which	O
were	O
discontinuous	O
in	O
the	O
default	O
topology	O
.	O
</s>
<s>
A	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
(	O
TVS	O
)	O
is	O
called	O
a	O
Mackey	B-Algorithm
space	I-Algorithm
if	O
its	O
topology	O
is	O
the	O
same	O
as	O
the	O
Mackey	B-Algorithm
topology	I-Algorithm
.	O
</s>
<s>
The	O
Mackey	B-Algorithm
topology	I-Algorithm
is	O
the	O
opposite	O
of	O
the	O
weak	O
topology	O
,	O
which	O
is	O
the	O
coarsest	O
topology	O
on	O
a	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
which	O
preserves	O
the	O
continuity	O
of	O
all	O
linear	O
functions	O
in	O
the	O
continuous	O
dual	O
.	O
</s>
<s>
The	O
Mackey	B-Algorithm
–	I-Algorithm
Arens	I-Algorithm
theorem	I-Algorithm
states	O
that	O
all	O
possible	O
dual	B-Algorithm
topologies	I-Algorithm
are	O
finer	O
than	O
the	O
weak	O
topology	O
and	O
coarser	O
than	O
the	O
Mackey	B-Algorithm
topology	I-Algorithm
.	O
</s>
<s>
When	O
is	O
endowed	O
with	O
the	O
Mackey	B-Algorithm
topology	I-Algorithm
then	O
it	O
will	O
be	O
denoted	O
by	O
or	O
simply	O
or	O
if	O
no	O
ambiguity	O
can	O
arise	O
.	O
</s>
<s>
The	O
definition	O
of	O
the	O
Mackey	B-Algorithm
topology	I-Algorithm
for	O
a	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
(	O
TVS	O
)	O
is	O
a	O
specialization	O
of	O
the	O
above	O
definition	O
of	O
the	O
Mackey	B-Algorithm
topology	I-Algorithm
of	O
a	O
pairing	B-Algorithm
.	O
</s>
<s>
If	O
is	O
a	O
TVS	O
with	O
continuous	O
dual	O
space	O
then	O
the	O
evaluation	O
map	O
on	O
is	O
called	O
the	O
canonical	O
pairing	B-Algorithm
.	O
</s>
<s>
When	O
is	O
endowed	O
with	O
the	O
Mackey	B-Algorithm
topology	I-Algorithm
then	O
it	O
will	O
be	O
denoted	O
by	O
or	O
simply	O
if	O
no	O
ambiguity	O
can	O
arise	O
.	O
</s>
<s>
Every	O
metrizable	B-Algorithm
locally	B-Algorithm
convex	I-Algorithm
with	O
continuous	O
dual	O
carries	O
the	O
Mackey	B-Algorithm
topology	I-Algorithm
,	O
that	O
is	O
or	O
to	O
put	O
it	O
more	O
succinctly	O
every	O
metrizable	B-Algorithm
locally	B-Algorithm
convex	I-Algorithm
space	I-Algorithm
is	O
a	O
Mackey	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
Every	O
Hausdorff	O
barreled	B-Algorithm
locally	B-Algorithm
convex	I-Algorithm
space	I-Algorithm
is	O
Mackey	O
.	O
</s>
<s>
The	O
Mackey	B-Algorithm
topology	I-Algorithm
has	O
an	O
application	O
in	O
economies	O
with	O
infinitely	O
many	O
commodities	O
.	O
</s>
