<s>
In	O
functional	B-Application
analysis	I-Application
,	O
a	O
discipline	O
within	O
mathematics	O
,	O
a	O
locally	B-Algorithm
convex	I-Algorithm
topological	I-Algorithm
vector	I-Algorithm
space	I-Algorithm
(	O
TVS	O
)	O
is	O
said	O
to	O
be	O
infrabarrelled	O
(	O
also	O
spelled	O
infrabarreled	B-Algorithm
)	O
if	O
every	O
bounded	B-Algorithm
absorbing	B-Algorithm
barrel	B-Algorithm
is	O
a	O
neighborhood	O
of	O
the	O
origin	O
.	O
</s>
<s>
If	O
is	O
a	O
Hausdorff	O
locally	B-Algorithm
convex	I-Algorithm
space	I-Algorithm
then	O
the	O
canonical	O
injection	O
from	O
into	O
its	O
bidual	O
is	O
a	O
topological	O
embedding	O
if	O
and	O
only	O
if	O
is	O
infrabarrelled	O
.	O
</s>
<s>
Every	O
quasi-complete	B-Algorithm
infrabarrelled	B-Algorithm
space	I-Algorithm
is	O
barrelled	O
.	O
</s>
<s>
Every	O
barrelled	B-Algorithm
space	I-Algorithm
is	O
infrabarrelled	O
.	O
</s>
<s>
A	O
closed	O
vector	O
subspace	O
of	O
an	O
infrabarrelled	B-Algorithm
space	I-Algorithm
is	O
,	O
however	O
,	O
not	O
necessarily	O
infrabarrelled	O
.	O
</s>
<s>
Every	O
product	O
and	O
locally	B-Algorithm
convex	I-Algorithm
direct	O
sum	O
of	O
any	O
family	O
of	O
infrabarrelled	B-Algorithm
spaces	I-Algorithm
is	O
infrabarrelled	O
.	O
</s>
<s>
Every	O
separated	O
quotient	O
of	O
an	O
infrabarrelled	B-Algorithm
space	I-Algorithm
is	O
infrabarrelled	O
.	O
</s>
