Compactness and Compactification | Original Article

ABSTRACT:

We recall all the important and useful theorems from calculus, which functions which are continuous on a closed and bounded interval take on a maximum and minimum value on that interval. The classic theorem of Heine-Borel-Lebesgue asset that every covering of such an interval by an open set has a finite subcover. In this chapter, we use this feature of closed and bounded subset to define the corresponding notion, compactness in a general topological space. In addition, we consider important variants of this notion sequential compactness and local compactness.