  # 4. Let K be a compact metric space, and Scc (K), where C (K) is the space of all complex continuousfunctions on K, equipped with the metric d (f,9)maxreK f() (x)|. Suppose that S is closed,pointwise bounded and equicontinuous. Show that S is compact.

Question help_outlineImage Transcriptionclose4. Let K be a compact metric space, and Scc (K), where C (K) is the space of all complex continuous functions on K, equipped with the metric d (f,9)maxreK f() (x)|. Suppose that S is closed, pointwise bounded and equicontinuous. Show that S is compact. fullscreen
check_circleExpert Solution
Step 1

To establish the compactness of the set S in the given topology

Step 2

Recall the  basic facts about compactness in metric spaces

Step 3

In view o the facts (1),(2) (3), it suffices to prove ...

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