Assume that A is a compact subset of a metric space (X,d), and B is a closed subset of A. Line 1: Last Line: Therefore, B is Compact. Options: Line 1:  Let F be an open cover of A Line 1:  Suppose that B is compact Line 1:  Let F be an open cover of B Line 1:  A is closed and bounded Last Line:  Therefore, there exists a finite subcover Last Line:  Therefore, B is closed and bounded Last Line:  Therefore, A is compact. Last Line:  Therefore, there exists a finite subcover G of F that covers A

Q: cise 2 Let X be a topological space. - Show that X itself is a Baire space. T

A: Given: X is a topological space. To Prove: We have to show that the topological space X itself is a…

Q: 2) Give an example of a metric space such that the closed ball Bå(x,r) is not an open set for any x…

A: To Find: Give an example of a metric space such that a closed ball B¯d(x,r) is not open set for any…

Q: 3) Give an example of a metric space such that some closed ball is an open subset. a metric space…

A:

Q: Let X be any nonempty set, and define (o if x = y. 11 if ry. Prove that (X. d) is a metric space.…

A:

Q: Topology Let X and Y be two compact spaces, show that X×Y is compact.

A: