Compact Spaces and Various Other Types of Spaces

Abstract

In this chapter we study various notions of compactness, including local compactness, countable compactness, pseudocompactness, paracompact-ness, etc. In view of the essential role played by compact spaces throughout topology and analysis, it is interesting to know when a topological space can be compactified; we consider this later in the chapter. We will also introduce other spaces, e.g., Baire spaces, k-spaces, which generalize compact spaces.