<s>
In	O
mathematics	O
,	O
specifically	O
in	O
topology	B-Architecture
and	O
functional	B-Application
analysis	I-Application
,	O
a	O
subspace	O
of	O
a	O
uniform	O
space	O
is	O
said	O
to	O
be	O
sequentially	B-Algorithm
complete	I-Algorithm
or	O
semi-complete	B-Algorithm
if	O
every	O
Cauchy	O
sequence	O
in	O
converges	O
to	O
an	O
element	O
in	O
.	O
</s>
<s>
is	O
called	O
sequentially	B-Algorithm
complete	I-Algorithm
if	O
it	O
is	O
a	O
sequentially	B-Algorithm
complete	I-Algorithm
subset	O
of	O
itself	O
.	O
</s>
<s>
Every	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
is	O
a	O
uniform	O
space	O
so	O
the	O
notion	O
of	O
sequential	O
completeness	O
can	O
be	O
applied	O
to	O
them	O
.	O
</s>
<s>
A	O
bounded	O
sequentially	B-Algorithm
complete	I-Algorithm
disk	O
in	O
a	O
Hausdorff	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
is	O
a	O
Banach	B-Algorithm
disk	I-Algorithm
.	O
</s>
<s>
A	O
Hausdorff	O
locally	O
convex	O
space	O
that	O
is	O
sequentially	B-Algorithm
complete	I-Algorithm
and	O
bornological	B-Algorithm
is	O
ultrabornological	B-Algorithm
.	O
</s>
<s>
Every	O
complete	O
space	O
is	O
sequentially	B-Algorithm
complete	I-Algorithm
but	O
not	O
conversely	O
.	O
</s>
<s>
A	O
metrizable	O
space	O
then	O
it	O
is	O
complete	O
if	O
and	O
only	O
if	O
it	O
is	O
sequentially	B-Algorithm
complete	I-Algorithm
.	O
</s>
<s>
Every	O
complete	B-Algorithm
topological	I-Algorithm
vector	I-Algorithm
space	I-Algorithm
is	O
quasi-complete	B-Algorithm
and	O
every	O
quasi-complete	B-Algorithm
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
is	O
sequentially	B-Algorithm
complete	I-Algorithm
.	O
</s>
