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Asked May 8, 2019
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3. Show that closed subspace of a complete metric space is complete.
4. Let f be a continuous mapping of a compact metric space X to metric space Y. Prove that
f (X) is compact.
A 1S
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3. Show that closed subspace of a complete metric space is complete. 4. Let f be a continuous mapping of a compact metric space X to metric space Y. Prove that f (X) is compact. A 1S

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Expert Answer

Step 1

To prove the statements on the topology of metric spaces under the given conditions

Step 2

3) Proof of "a closed subspace of a complete metric space is complete"

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Step 3

continuation of the...

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