<s>
In	O
mathematics	O
,	O
Delta-convergence	B-Algorithm
,	O
or	O
Δ-convergence	B-Algorithm
,	O
is	O
a	O
mode	O
of	O
convergence	O
in	O
metric	O
spaces	O
,	O
weaker	O
than	O
the	O
usual	O
metric	O
convergence	O
,	O
and	O
similar	O
to	O
(	O
but	O
distinct	O
from	O
)	O
the	O
weak	O
convergence	O
in	O
Banach	O
spaces	O
.	O
</s>
<s>
In	O
Hilbert	O
space	O
,	O
Delta-convergence	B-Algorithm
and	O
weak	O
convergence	O
coincide	O
.	O
</s>
<s>
In	O
particular	O
,	O
Delta-convergence	B-Algorithm
and	O
weak	O
convergence	O
coincide	O
if	O
is	O
a	O
Hilbert	O
space	O
.	O
</s>
<s>
The	O
Delta-compactness	O
theorem	O
is	O
similar	O
to	O
the	O
Banach	B-Algorithm
–	I-Algorithm
Alaoglu	I-Algorithm
theorem	I-Algorithm
for	O
weak	O
convergence	O
but	O
,	O
unlike	O
the	O
Banach-Alaoglu	B-Algorithm
theorem	I-Algorithm
(	O
in	O
the	O
non-separable	O
case	O
)	O
its	O
proof	O
does	O
not	O
depend	O
on	O
the	O
Axiom	O
of	O
Choice	O
.	O
</s>
