<s>
In	O
mathematics	O
,	O
particularly	O
in	O
functional	B-Application
analysis	I-Application
,	O
a	O
Mackey	B-Algorithm
space	I-Algorithm
is	O
a	O
locally	B-Algorithm
convex	I-Algorithm
topological	I-Algorithm
vector	I-Algorithm
space	I-Algorithm
X	O
such	O
that	O
the	O
topology	B-Architecture
of	O
X	O
coincides	O
with	O
the	O
Mackey	B-Algorithm
topology	I-Algorithm
τ( X	O
,	O
X′	O
)	O
,	O
the	O
finest	O
topology	B-Architecture
which	O
still	O
preserves	O
the	O
continuous	O
dual	O
.	O
</s>
<s>
Examples	O
of	O
locally	B-Algorithm
convex	I-Algorithm
spaces	I-Algorithm
that	O
are	O
Mackey	B-Algorithm
spaces	I-Algorithm
include	O
:	O
</s>
<s>
In	O
particular	O
,	O
all	O
Fréchet	B-Algorithm
spaces	I-Algorithm
,	O
including	O
all	O
Banach	O
spaces	O
and	O
specifically	O
Hilbert	O
spaces	O
,	O
are	O
Mackey	B-Algorithm
spaces	I-Algorithm
.	O
</s>
<s>
The	O
product	O
,	O
locally	B-Algorithm
convex	I-Algorithm
direct	O
sum	O
,	O
and	O
the	O
inductive	O
limit	O
of	O
a	O
family	O
of	O
Mackey	B-Algorithm
spaces	I-Algorithm
is	O
a	O
Mackey	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
A	O
locally	B-Algorithm
convex	I-Algorithm
space	I-Algorithm
with	O
continuous	O
dual	O
is	O
a	O
Mackey	B-Algorithm
space	I-Algorithm
if	O
and	O
only	O
if	O
each	O
convex	O
and	O
-relatively	O
compact	O
subset	O
of	O
is	O
equicontinuous	O
.	O
</s>
<s>
The	O
completion	O
of	O
a	O
Mackey	B-Algorithm
space	I-Algorithm
is	O
again	O
a	O
Mackey	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
A	O
separated	O
quotient	O
of	O
a	O
Mackey	B-Algorithm
space	I-Algorithm
is	O
again	O
a	O
Mackey	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
A	O
Mackey	B-Algorithm
space	I-Algorithm
need	O
not	O
be	O
separable	O
,	O
complete	O
,	O
quasi-barrelled	B-Algorithm
,	O
nor	O
-quasi-barrelled	O
.	O
</s>
