Show that if Y is locally compact Hausdorff, then composition of maps C(X, Y) × C(Y, Z) ? C(X, Z) is continuous, provided the compact-open topology is used throughout. [Hint: If g ? f ? S(C, U), find V such that f(C) ? V and g(V?) ? U.]
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Let Y be a locally compact Hausdorff space. Show more…
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