![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)
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 (
![general topology - Help understanding why a complete, totally bounded metric space implies every infinite subset has a limit point - Mathematics Stack Exchange general topology - Help understanding why a complete, totally bounded metric space implies every infinite subset has a limit point - Mathematics Stack Exchange](https://i.stack.imgur.com/WG0xn.png)
general topology - Help understanding why a complete, totally bounded metric space implies every infinite subset has a limit point - Mathematics Stack Exchange
![SOLVED: Definition: Suppose (X, dx) and (Y, dy) are metric spaces and X is compact. Let C(X, Y) be the set of all continuous functions from X into Y and let D : SOLVED: Definition: Suppose (X, dx) and (Y, dy) are metric spaces and X is compact. Let C(X, Y) be the set of all continuous functions from X into Y and let D :](https://cdn.numerade.com/ask_images/94f230ab52244c259491adcb8e9625c7.jpg)
SOLVED: Definition: Suppose (X, dx) and (Y, dy) are metric spaces and X is compact. Let C(X, Y) be the set of all continuous functions from X into Y and let D :
![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)