3) A (somewhat artificial) example of a semi-reflexive space that is not reflexive is obtained as follows: let "Y" be an infinite dimensional reflexive Banach space, and let "X" be the topological vector space , that is, the vector space "Y" equipped with the weak topology. Then the continuous dual of "X" and are the same set of functionals, and bounded subsets of "X" ("i.e.", weakly bounded subsets of "Y") are norm-bounded, hence the Banach space is the strong dual of "X". Since "Y" is reflexive, the continuous dual of is equal to the image "J"("X") of "X" under the canonical embedding "J", but the topology on "X" (the weak topology of "Y") is not the strong topology , that is equal to the norm topology of "Y".