This study aims to redefine the weak topology on
σ
(
X
M
*
,
X
M
*
*
)
on a specific topological dual space (modular dual space XM
*
) this is weak topology generated by all linear bounded functional on XM
*
, but we interested in a subspace of this topology generated by XM
called weak* topology on XM
*
, it follows from that the modular space XM
over the field K can be embedded in
X
M
*
*
by using the canonical map, we denoted to this topology by
σ
(
X
M
*
,
X
M
)
. After that, we checked the weak* topology is Hausdorff and investigated some properties, finally, we showed that under which condition the strong topology and the weak* topology coincided.