Of all the invariants of topology compactness is undoubtedly the most important. To appreciate it fully one has to look at it in several different ways. The way I have chosen to define it in the first instance follows on very naturally from the discussion of closed functions at the end of the previous chapter. Once we have established its main properties and considered some examples we will show how compactness can be characterized in other ways. Of these the characterization in terms of the existence of finite subcoverings of open coverings is certainly the best known.
Unable to display preview. Download preview PDF.