<s>
In	O
mathematical	O
analysis	O
,	O
a	O
thin	B-Algorithm
set	I-Algorithm
is	O
a	O
subset	O
of	O
n-dimensional	O
complex	B-Algorithm
space	I-Algorithm
Cn	O
with	O
the	O
property	O
that	O
each	O
point	O
has	O
a	O
neighbourhood	O
on	O
which	O
some	O
non-zero	O
holomorphic	O
function	O
vanishes	O
.	O
</s>
<s>
Since	O
the	O
set	O
on	O
which	O
a	O
holomorphic	O
function	O
vanishes	O
is	O
closed	O
and	O
has	O
empty	O
interior	O
(	O
by	O
the	O
Identity	O
theorem	O
)	O
,	O
a	O
thin	B-Algorithm
set	I-Algorithm
is	O
nowhere	O
dense	O
,	O
and	O
the	O
closure	O
of	O
a	O
thin	B-Algorithm
set	I-Algorithm
is	O
also	O
thin	O
.	O
</s>
<s>
The	O
fine	O
topology	O
was	O
introduced	O
in	O
1940	O
by	O
Henri	O
Cartan	O
to	O
aid	O
in	O
the	O
study	O
of	O
thin	B-Algorithm
sets	I-Algorithm
.	O
</s>
