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147 prove the following proposition 1412 a let xd be...

Question: 147 prove the following proposition 1412 a let xd be...

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1.4.7 Prove the following Proposition 1.4.12. (a) Let (X,d) be a metric space, and let (Y, dlyxY) be a subspace of (X, d). If (Y, dlyxY) is complete, then Tnust be closed 2.TI. Л. (b) Conversely, suppose that (X, d) is a complete metric space, and y is a closed subset of X. Then the subspace (Υ.dyxx) is also complete. 1.4.7 Prove the following Proposition 1.4.12. (a) Let (X,d) be a metric space, and let (Y, dlyxY) be a subspace of (X, d). If (Y, dlyxY) is complete, then Tnust be closed 2.TI. Л. (b) Conversely, suppose that (X, d) is a complete metric space, and y is a closed subset of X. Then the subspace (Υ.dyxx) is also complete.

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