<s>
In	O
functional	B-Application
analysis	I-Application
and	O
related	O
areas	O
of	O
mathematics	O
a	O
FK-space	B-Algorithm
or	O
Fréchet	O
coordinate	O
space	O
is	O
a	O
sequence	B-Algorithm
space	I-Algorithm
equipped	O
with	O
a	O
topological	O
structure	O
such	O
that	O
it	O
becomes	O
a	O
Fréchet	B-Algorithm
space	I-Algorithm
.	O
</s>
<s>
FK-spaces	B-Algorithm
with	O
a	O
normable	O
topology	O
are	O
called	O
BK-spaces	O
.	O
</s>
<s>
There	O
exists	O
only	O
one	O
topology	O
to	O
turn	O
a	O
sequence	B-Algorithm
space	I-Algorithm
into	O
a	O
Fréchet	B-Algorithm
space	I-Algorithm
,	O
namely	O
the	O
topology	O
of	O
pointwise	B-Algorithm
convergence	I-Algorithm
.	O
</s>
<s>
Thus	O
the	O
name	O
coordinate	O
space	O
because	O
a	O
sequence	O
in	O
an	O
FK-space	B-Algorithm
converges	O
if	O
and	O
only	O
if	O
it	O
converges	O
for	O
each	O
coordinate	O
.	O
</s>
<s>
FK-spaces	B-Algorithm
are	O
examples	O
of	O
topological	B-Architecture
vector	I-Architecture
spaces	I-Architecture
.	O
</s>
<s>
They	O
are	O
important	O
in	O
summability	B-Algorithm
theory	I-Algorithm
.	O
</s>
<s>
A	O
FK-space	B-Algorithm
is	O
a	O
sequence	B-Algorithm
space	I-Algorithm
,	O
that	O
is	O
a	O
linear	O
subspace	O
of	O
vector	O
space	O
of	O
all	O
complex	B-Algorithm
valued	I-Algorithm
sequences	I-Algorithm
,	O
equipped	O
with	O
the	O
topology	O
of	O
pointwise	B-Algorithm
convergence	I-Algorithm
.	O
</s>
<s>
The	O
sequence	B-Algorithm
space	I-Algorithm
of	O
all	O
complex	B-Algorithm
valued	I-Algorithm
sequences	I-Algorithm
is	O
trivially	O
an	O
FK-space	B-Algorithm
.	O
</s>
<s>
Then	O
is	O
again	O
an	O
FK-space	B-Algorithm
.	O
</s>
