( 見 Munkers 的 Topology, second edition. P.286 )
書上有定理(P.285)
Theorem 46.8. Let X be a space and let (Y,d) be a metric space. On the set
C(X,Y) , the compact-open topology and the topology of compact convergence
coincide.
(P.286)
Corollary 46.9. Let Y be a metric space. The compact convergence topology on
C(X,Y) does not depend on the metric of Y. ......
上面的 Corollary 看不懂，
雖然 TH 46.8 說明了the compact-open topology 和
the topology of compact convergence 是一樣的，但是若 Y 的 metric 改變，還是會
影響 compact-open topology，也就影響 compact convergence topology.
另外我也想過，先給定 X: topological space, (Y,d): metric space. f in C(X,Y)
若 d' 為 Y 的另一個 metric，考慮 f: X → (Y,d') . 那麼 f 可能不是連續函數.
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