<s>
In	O
functional	B-Application
analysis	I-Application
and	O
related	O
areas	O
of	O
mathematics	O
,	O
a	O
quasi-ultrabarrelled	B-Algorithm
space	I-Algorithm
is	O
a	O
topological	B-Architecture
vector	I-Architecture
spaces	I-Architecture
(	O
TVS	O
)	O
for	O
which	O
every	O
bornivorous	B-Algorithm
ultrabarrel	I-Algorithm
is	O
a	O
neighbourhood	O
of	O
the	O
origin	O
.	O
</s>
<s>
A	O
subset	O
B0	O
of	O
a	O
TVS	O
X	O
is	O
called	O
a	O
bornivorous	B-Algorithm
ultrabarrel	I-Algorithm
if	O
it	O
is	O
a	O
closed	O
,	O
balanced	O
,	O
and	O
bornivorous	B-Algorithm
subset	O
of	O
X	O
and	O
if	O
there	O
exists	O
a	O
sequence	O
of	O
closed	O
balanced	O
and	O
bornivorous	B-Algorithm
subsets	O
of	O
X	O
such	O
that	O
Bi+1	O
+	O
Bi+1	O
Bi	O
for	O
all	O
i	O
=	O
0	O
,	O
1	O
,	O
....	O
</s>
<s>
A	O
TVS	O
X	O
is	O
called	O
quasi-ultrabarrelled	O
if	O
every	O
bornivorous	B-Algorithm
ultrabarrel	I-Algorithm
in	O
X	O
is	O
a	O
neighbourhood	O
of	O
the	O
origin	O
.	O
</s>
<s>
A	O
locally	B-Algorithm
convex	I-Algorithm
quasi-ultrabarrelled	B-Algorithm
space	I-Algorithm
is	O
quasi-barrelled	B-Algorithm
.	O
</s>
<s>
Ultrabarrelled	B-Algorithm
spaces	I-Algorithm
and	O
ultrabornological	B-Algorithm
spaces	I-Algorithm
are	O
quasi-ultrabarrelled	O
.	O
</s>
<s>
Complete	O
and	O
metrizable	O
TVSs	O
are	O
quasi-ultrabarrelled	O
.	O
</s>
