Weakly continuous functions of Baire class 1.

Rao, T. S. S. R. K.. "Weakly continuous functions of Baire class 1.." Extracta Mathematicae 15.1 (2000): 207-212. <http://eudml.org/doc/38625>.

@article{Rao2000,
abstract = {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 --&gt; f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.},
author = {Rao, T. S. S. R. K.},
journal = {Extracta Mathematicae},
keywords = {Espacios de Banach; Espacio de Banach localmente compacto; Funciones casi continuas; Espacios de Baire; countable chain condition},
language = {eng},
number = {1},
pages = {207-212},
title = {Weakly continuous functions of Baire class 1.},
url = {http://eudml.org/doc/38625},
volume = {15},
year = {2000},
}

TY - JOUR
AU - Rao, T. S. S. R. K.
TI - Weakly continuous functions of Baire class 1.
JO - Extracta Mathematicae
PY - 2000
VL - 15
IS - 1
SP - 207
EP - 212
AB - 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 --&gt; f pointwise w.r.t. the norm topology on X. Such a function f is said to be of Baire class 1.
LA - eng
KW - Espacios de Banach; Espacio de Banach localmente compacto; Funciones casi continuas; Espacios de Baire; countable chain condition
UR - http://eudml.org/doc/38625
ER -