%0 Journal Article
%A Ferrera Cuesta, Juan
%T Spaces of weakly continuous functions.
%D 1982
%@ 0030-8730
%U https://hdl.handle.net/20.500.14352/64624
%X This paper is very much in the spirit of a paper by H. Corson [Trans. Amer. Math. Soc. 101 (1961),1–15; MR0132375 (24 2220)]. Let E be a real Banach space. The bw-topology on E is the finesttopology which agrees with the weak topology on all bounded subsets of E. Cwb(E) [Cwbu(E)]is the set of real functions which are weakly continuous [weakly uniformly continuous] on allbounded sets in E. Cwb(E) is always barrelled; a sufficient condition is given for Cwb(E) to bebornological (under the compact-open topology). As a main result, the following are shown to beequivalent: (1) E is reflexive; (ii) Cwbu(E) is a Fr´echet space; (iii) Cwbu(E) is a Pt´ak space; (iv)Cwbu(E) is complete; (v) Cwbu(E) is barrelled; (vi) Cwbu(E) = Cwb(E).
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