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 {fa} contained in C(K,X) (space of norm continuous functions) such that fa --> f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.
@article{urn:eudml:doc:38625,
title = {Weakly continuous functions of Baire class 1.},
journal = {Extracta Mathematicae},
volume = {15},
year = {2000},
pages = {207-212},
zbl = {1004.54014},
mrnumber = {MR1792989},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38625}
}
Rao, T. S. S. R. K. Weakly continuous functions of Baire class 1.. Extracta Mathematicae, Tome 15 (2000) pp. 207-212. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38625/