Weak Topology - The Weak-* Topology

The Weak-* Topology

A space X can be embedded into the double dual X** by

where

Thus T : XX** 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.

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