... relativizationof the weak topolog y of E, and taking τ as the weak topology of E.Duetothekindof continuity we are assuming for A, the function x →A(x),x turns out to be weaklycontinuous (see the proof ... y)iscontinuousforally ∈ B1,wethenrealize that the restriction of f to X0× B1satisfies the hypotheses of Theorem 3, B1beingconsidered with the relativization of the strong topology. Hence, the ... against(27). Hence, we have A(x),A(x)=α(x)forallx ∈ C. At this point, the conclusion fol-lows at once from Theorem 7,takingg = A|C. Remark 9. It would be interesting to know whether Theorem...