<s>
The	O
grid	B-Algorithm
cell	I-Algorithm
topology	I-Algorithm
is	O
studied	O
in	O
digital	B-Algorithm
topology	I-Algorithm
as	O
part	O
of	O
the	O
theoretical	O
basis	O
for	O
(	O
low-level	O
)	O
algorithms	O
in	O
computer	B-General_Concept
image	I-General_Concept
analysis	I-General_Concept
or	O
computer	O
graphics	O
.	O
</s>
<s>
The	O
elements	O
of	O
the	O
n-dimensional	O
grid	B-Algorithm
cell	I-Algorithm
topology	I-Algorithm
(	O
n	O
≥	O
1	O
)	O
are	O
all	O
n-dimensional	O
grid	O
cubes	O
and	O
their	O
k-dimensional	O
faces	O
(	O
for	O
0	O
≤	O
k	O
≤	O
n1	O
)	O
;	O
between	O
these	O
a	O
partial	O
order	O
A	O
≤	O
B	O
is	O
defined	O
if	O
A	O
is	O
a	O
subset	O
of	O
B	O
(	O
and	O
thus	O
also	O
dim(A )	O
≤	O
dim(B )	O
)	O
.	O
</s>
<s>
The	O
grid	B-Algorithm
cell	I-Algorithm
topology	I-Algorithm
is	O
the	O
Alexandrov	O
topology	B-Architecture
(	O
open	O
sets	O
are	O
up-sets	O
)	O
with	O
respect	O
to	O
this	O
partial	O
order	O
.	O
</s>
<s>
(	O
See	O
also	O
poset	O
topology	B-Architecture
.	O
)	O
</s>
<s>
Alexandrov	O
and	O
Hopf	O
first	O
introduced	O
the	O
grid	B-Algorithm
cell	I-Algorithm
topology	I-Algorithm
,	O
for	O
the	O
two-dimensional	O
case	O
,	O
within	O
an	O
exercise	O
in	O
their	O
text	O
Topologie	O
I	O
(	O
1935	O
)	O
.	O
</s>
<s>
It	O
is	O
related	O
to	O
digital	B-Algorithm
manifolds	I-Algorithm
.	O
</s>
