Weakly continuous functions of Baire class 1.
T. S. S. R. K. Rao (2000)
Extracta Mathematicae
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For a compact Hausdorff space K and a Banach space X, let WC(K,X) denote the space of X-valued functions defined on K, that are continuous when X has the weak topology. In this note by a simple Banach space theoretic argument, we show that given f belonging to WC(K,X) there exists a net {f} contained in C(K,X) (space of norm continuous functions) such that f --> f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.