Semi-smooth points in some classical function spaces (Q824363)

Let \(\mathcal{T}\) be a locally compact Hausdorff space and let \(E\) be a real normed linear space. Also, let \(\mathcal{C}_0 (\mathcal{T}, E)\) denote the space of all continuous functions \(f\) from \(\mathcal{T}\) to \(E\) which vanish at infinity. The authors study the semi-smooth points of the unit ball of \(\mathcal{C}_0 (\mathcal{T}, E)\). They also obtain necessary and sufficient condition for semi-smoothness. Finally, the authors study semi-smooth points in normed spaces.