On the topology of pointwise convergence on the ... - CARMA
On the topology of pointwise convergence on the ... - CARMA
On the topology of pointwise convergence on the ... - CARMA
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Corollary 3 Suppose that A is a topological space with countabletightness that possesses a rich family <str<strong>on</strong>g>of</str<strong>on</strong>g> Baire subspacesand suppose that K is a compact Hausdorff space. Then forany boundary <str<strong>on</strong>g>of</str<strong>on</strong>g> (C(K), ‖ · ‖ ∞ ) and any c<strong>on</strong>tinuous functi<strong>on</strong>f : A → (C(K), σ(C(K), B)) <str<strong>on</strong>g>the</str<strong>on</strong>g>re exists a dense subset D<str<strong>on</strong>g>of</str<strong>on</strong>g> A such that f is c<strong>on</strong>tinuous with respect to <str<strong>on</strong>g>the</str<strong>on</strong>g> ‖ · ‖ ∞ -<str<strong>on</strong>g>topology</str<strong>on</strong>g> at each point <str<strong>on</strong>g>of</str<strong>on</strong>g> D.——————————– The End ——————————–
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