Displaying similar documents to “Weakly compactly generated Frechet spaces.”

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.

Pointwise compactness and continuity of the integral.

G. Vera (1996)

Revista Matemática de la Universidad Complutense de Madrid

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In this paper we bring together the different known ways of establishing the continuity of the integral over a uniformly integrable set of functions endowed with the topology of pointwise convergence. We use these techniques to study Pettis integrability, as well as compactness in C(K) spaces endowed with the topology of pointwise convergence on a dense subset D in K.