The Weak-* Topology
A space X can be embedded into the double dual X** by
where
Thus T : X → X** is an injective linear mapping, though not necessarily surjective (spaces for which this canonical embedding is surjective are called reflexive). The weak-* topology on X* is the weak topology induced by the image of T: T(X) ⊂ X**. In other words, it is the coarsest topology such that the maps Tx from X* to the base field R or C remain continuous.
Read more about this topic: Weak Topology
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