Abstract
The investigations of the smooth points in the spaces of continuous function were started by Banach in 1932 considering function space mathcal {C}(Omega ). Singer and Sundaresan extended the result of Banach to the space of vector valued continuous functions mathcal {C}(mathcal {T},E), where mathcal {T} is a compact metric space. The aim of this paper is to present a description of semi-smooth points in spaces of continuous functions mathcal {C}_0(mathcal {T},E) (instead of smooth points). Moreover, we also find necessary and sufficient condition for semi-smoothness in the general case.
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