![SOLVED: (a) Prove that every compact metric space is a complete metric space, but the converse is not true. (b) Let A, B ∈ R^3 be two nonempty subsets. Show that if SOLVED: (a) Prove that every compact metric space is a complete metric space, but the converse is not true. (b) Let A, B ∈ R^3 be two nonempty subsets. Show that if](https://cdn.numerade.com/ask_images/7a664fcb210242fcb1b304108e35d3f5.jpg)
SOLVED: (a) Prove that every compact metric space is a complete metric space, but the converse is not true. (b) Let A, B ∈ R^3 be two nonempty subsets. Show that if
![real analysis - Metric space, I would like to rewrite this proof, completeness and compactness - Mathematics Stack Exchange real analysis - Metric space, I would like to rewrite this proof, completeness and compactness - Mathematics Stack Exchange](https://i.stack.imgur.com/BMooi.png)
real analysis - Metric space, I would like to rewrite this proof, completeness and compactness - Mathematics Stack Exchange
![SOLVED: Show that the metric space (X, dx) is complete if every closed ball in X is complete. State an equivalent condition for the metric space (X, dx) to be compact. Let ( SOLVED: Show that the metric space (X, dx) is complete if every closed ball in X is complete. State an equivalent condition for the metric space (X, dx) to be compact. Let (](https://cdn.numerade.com/ask_images/b48c3ba1855f408c9a835c94744d45c0.jpg)