Notes:Compactness and sequences
From Maths
Analysis: Part 1 - Elements by Krzysztof Maurin has a great bit on compactness! It uses sequences in a metric space
Topology by Munkres has a great bit on compactness! It uses open sets in topology.
I need to distinguish (fail to unite) the two. There are notes on the Sequential compactness page - annoyingly no references - YET