Countable Compactness in Topological Spaces- part 3

⬗ Prove that a metric space is compact iff it is countably compact. ⬗ Prove that every continuous, real-valued function on a countably compact space is bounded and attains its extrema. .......................................................................................... M.Sc. Mathematics Semester 2 Advanced Topology Reference Book: Introduction to General Topology by K D Joshi