<s>
In	O
mathematics	O
,	O
specifically	O
in	O
functional	B-Application
analysis	I-Application
,	O
a	O
family	O
of	O
subsets	O
a	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
(	O
TVS	O
)	O
is	O
said	O
to	O
be	O
saturated	O
if	O
contains	O
a	O
non-empty	O
subset	O
of	O
and	O
if	O
for	O
every	O
the	O
following	O
conditions	O
all	O
hold	O
:	O
</s>
<s>
The	O
intersection	O
of	O
an	O
arbitrary	O
family	O
of	O
saturated	B-Algorithm
families	I-Algorithm
is	O
a	O
saturated	B-Algorithm
family	I-Algorithm
.	O
</s>
<s>
Since	O
the	O
power	O
set	O
of	O
is	O
saturated	O
,	O
any	O
given	O
non-empty	O
family	O
of	O
subsets	O
of	O
containing	O
at	O
least	O
one	O
non-empty	O
set	O
,	O
the	O
saturated	B-Algorithm
hull	I-Algorithm
of	O
is	O
well-defined	O
.	O
</s>
<s>
The	O
set	O
of	O
all	O
bounded	B-Algorithm
subsets	O
of	O
a	O
topological	B-Architecture
vector	I-Architecture
space	I-Architecture
is	O
a	O
saturated	B-Algorithm
family	I-Algorithm
.	O
</s>
