Thread: Compactness and sequentiall compactness

is there a difference between compactness and sequential compactness in a metric space or are these two terms simply interchangable?
From what i can understand sequentially compact means that every subsequence has a convergent subsequence within the space and compact is the topological definition with repsect to subcovers which i have read twenty times but have no idea what it means. Can anyuone clarify?

Originally Posted by johnnys

is there a difference between compactness and sequential compactness in a metric space or are these two terms simply interchangable? Sequentially compact means that every subsequence has a convergent subsequence within the space and compact is the topological definition with repsect to subcovers which i have read twenty times but have no idea what it means. Can anyuone clarify?

In a metric space sequentially compactness is equivalent to compactness.