<s>
In	O
functional	B-Application
analysis	I-Application
,	O
a	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
(	O
TVS	O
)	O
is	O
said	O
to	O
be	O
quasi-complete	B-Algorithm
or	O
boundedly	O
complete	O
if	O
every	O
closed	O
and	O
bounded	B-Algorithm
subset	O
is	O
complete	O
.	O
</s>
<s>
Every	O
quasi-complete	B-Algorithm
TVS	O
is	O
sequentially	B-Algorithm
complete	I-Algorithm
.	O
</s>
<s>
In	O
a	O
quasi-complete	B-Algorithm
locally	B-Algorithm
convex	I-Algorithm
space	I-Algorithm
,	O
the	O
closure	O
of	O
the	O
convex	O
hull	O
of	O
a	O
compact	O
subset	O
is	O
again	O
compact	O
.	O
</s>
<s>
In	O
a	O
quasi-complete	B-Algorithm
Hausdorff	O
TVS	O
,	O
every	O
precompact	O
subset	O
is	O
relatively	O
compact	O
.	O
</s>
<s>
If	O
is	O
a	O
normed	O
space	O
and	O
is	O
a	O
quasi-complete	B-Algorithm
locally	B-Algorithm
convex	I-Algorithm
TVS	O
then	O
the	O
set	O
of	O
all	O
compact	O
linear	O
maps	O
of	O
into	O
is	O
a	O
closed	O
vector	O
subspace	O
of	O
.	O
</s>
<s>
Every	O
quasi-complete	B-Algorithm
infrabarrelled	B-Algorithm
space	I-Algorithm
is	O
barreled	O
.	O
</s>
<s>
If	O
is	O
a	O
quasi-complete	B-Algorithm
locally	B-Algorithm
convex	I-Algorithm
space	I-Algorithm
then	O
every	O
weakly	O
bounded	B-Algorithm
subset	O
of	O
the	O
continuous	O
dual	O
space	O
is	O
strongly	B-Algorithm
bounded	I-Algorithm
.	O
</s>
<s>
A	O
quasi-complete	B-Algorithm
nuclear	B-Algorithm
space	I-Algorithm
then	O
has	O
the	O
Heine	O
–	O
Borel	O
property	O
.	O
</s>
<s>
Every	O
complete	O
TVS	O
is	O
quasi-complete	B-Algorithm
.	O
</s>
<s>
The	O
product	O
of	O
any	O
collection	O
of	O
quasi-complete	B-Algorithm
spaces	I-Algorithm
is	O
again	O
quasi-complete	B-Algorithm
.	O
</s>
<s>
The	O
projective	O
limit	O
of	O
any	O
collection	O
of	O
quasi-complete	B-Algorithm
spaces	I-Algorithm
is	O
again	O
quasi-complete	B-Algorithm
.	O
</s>
<s>
Every	O
semi-reflexive	O
space	O
is	O
quasi-complete	B-Algorithm
.	O
</s>
<s>
The	O
quotient	O
of	O
a	O
quasi-complete	B-Algorithm
space	I-Algorithm
by	O
a	O
closed	O
vector	O
subspace	O
may	O
fail	O
to	O
be	O
quasi-complete	B-Algorithm
.	O
</s>
<s>
There	O
exists	O
an	O
LB-space	B-Algorithm
that	O
is	O
not	O
quasi-complete	B-Algorithm
.	O
</s>
