a set spans space

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X is BANACH space and $T(t)_{t\geq0}$ un C$_{0}$-semigroupe sur X.
U(x)= $int \{ y\in X, \exists (tn)\nearrow \infty \ limT_{tn}(x)=y\}$
My question is how to prove That if $U(x)\neq \emptyset$ then span(U(x))=X