<s>
In	O
mathematics	O
,	O
particularly	O
in	O
functional	B-Application
analysis	I-Application
,	O
a	O
webbed	B-Algorithm
space	I-Algorithm
is	O
a	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
designed	O
with	O
the	O
goal	O
of	O
allowing	O
the	O
results	O
of	O
the	O
open	O
mapping	O
theorem	O
and	O
the	O
closed	O
graph	O
theorem	O
to	O
hold	O
for	O
a	O
wider	O
class	O
of	O
linear	B-Architecture
maps	I-Architecture
whose	O
codomains	O
are	O
webbed	B-Algorithm
spaces	I-Algorithm
.	O
</s>
<s>
Let	O
be	O
a	O
Hausdorff	O
locally	B-Algorithm
convex	I-Algorithm
topological	I-Algorithm
vector	I-Algorithm
space	I-Algorithm
.	O
</s>
<s>
Stratum	O
2	O
:	O
For	O
each	O
disk	O
in	O
the	O
first	O
stratum	O
,	O
there	O
must	O
exists	O
a	O
sequence	O
of	O
disks	O
in	O
such	O
that	O
for	O
every	O
:	O
and	O
absorbs	B-Algorithm
The	O
sets	O
will	O
form	O
the	O
second	O
stratum	O
.	O
</s>
<s>
Stratum	O
3	O
:	O
To	O
each	O
disk	O
in	O
the	O
second	O
stratum	O
,	O
assign	O
another	O
sequence	O
of	O
disks	O
in	O
satisfying	O
analogously	O
defined	O
properties	O
;	O
explicitly	O
,	O
this	O
means	O
that	O
for	O
every	O
:	O
and	O
absorbs	B-Algorithm
The	O
sets	O
form	O
the	O
third	O
stratum	O
.	O
</s>
<s>
A	O
Hausdorff	O
locally	B-Algorithm
convex	I-Algorithm
topological	I-Algorithm
vector	I-Algorithm
space	I-Algorithm
on	O
which	O
a	O
web	O
can	O
be	O
defined	O
is	O
called	O
a	O
.	O
</s>
<s>
Fréchet	B-Algorithm
spaces	I-Algorithm
.	O
</s>
<s>
Projective	O
limits	O
and	O
inductive	O
limits	O
of	O
sequences	O
of	O
webbed	B-Algorithm
spaces	I-Algorithm
.	O
</s>
<s>
A	O
sequentially	O
closed	O
vector	O
subspace	O
of	O
a	O
webbed	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
Countable	O
products	O
of	O
webbed	B-Algorithm
spaces	I-Algorithm
.	O
</s>
<s>
A	O
Hausdorff	O
quotient	O
of	O
a	O
webbed	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
The	O
image	O
of	O
a	O
webbed	B-Algorithm
space	I-Algorithm
under	O
a	O
sequentially	O
continuous	O
linear	B-Architecture
map	I-Architecture
if	O
that	O
image	O
is	O
Hausdorff	O
.	O
</s>
<s>
The	O
bornologification	B-Algorithm
of	O
a	O
webbed	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
The	O
continuous	O
dual	O
space	O
of	O
a	O
metrizable	O
locally	B-Algorithm
convex	I-Algorithm
space	I-Algorithm
endowed	O
with	O
the	O
strong	B-Algorithm
dual	I-Algorithm
topology	I-Algorithm
is	O
webbed	O
.	O
</s>
<s>
If	O
is	O
the	O
strict	O
inductive	O
limit	O
of	O
a	O
denumerable	O
family	O
of	O
locally	B-Algorithm
convex	I-Algorithm
metrizable	O
spaces	O
,	O
then	O
the	O
continuous	O
dual	O
space	O
of	O
with	O
the	O
strong	B-Algorithm
topology	I-Algorithm
is	O
webbed	O
.	O
</s>
<s>
So	O
in	O
particular	O
,	O
the	O
strong	B-Algorithm
duals	I-Algorithm
of	O
locally	B-Algorithm
convex	I-Algorithm
metrizable	O
spaces	O
are	O
webbed	O
.	O
</s>
<s>
If	O
is	O
a	O
webbed	B-Algorithm
space	I-Algorithm
,	O
then	O
any	O
Hausdorff	O
locally	B-Algorithm
convex	I-Algorithm
topology	I-Algorithm
weaker	O
than	O
this	O
(	O
webbed	O
)	O
topology	O
is	O
also	O
webbed	O
.	O
</s>
<s>
If	O
the	O
spaces	O
are	O
not	O
locally	B-Algorithm
convex	I-Algorithm
,	O
then	O
there	O
is	O
a	O
notion	O
of	O
web	O
where	O
the	O
requirement	O
of	O
being	O
a	O
disk	O
is	O
replaced	O
by	O
the	O
requirement	O
of	O
being	O
balanced	O
.	O
</s>
