<s>
If	O
(	O
)	O
is	O
the	O
usual	O
space	O
of	O
real	O
valued	O
functions	O
used	O
to	O
define	O
Lp	O
spaces	O
then	O
is	O
countably	O
order	B-Algorithm
complete	I-Algorithm
(	O
that	O
is	O
,	O
each	O
subset	O
that	O
is	O
bounded	O
above	O
has	O
a	O
supremum	O
)	O
but	O
in	O
general	O
is	O
not	O
order	B-Algorithm
complete	I-Algorithm
.	O
</s>
<s>
If	O
is	O
the	O
vector	O
subspace	O
of	O
all	O
-null	O
functions	O
then	O
is	O
a	O
solid	B-Algorithm
subset	I-Algorithm
of	O
that	O
is	O
a	O
band	O
.	O
</s>
