ABSTRACT
This chapter explores some deeper questions about sequential compactness and its connection to open sets. It proves propositions in set theory in a very different manner. The union of two open sets is open and countable unions of open sets are open. Unions need not be over countable index sets. The rational numbers are countable and uncountable unions of open sets are open. The complement of a finite intersection is provided as the union of the individual complements. The intersection of a finite number of closed sets is closed. The chapter discusses the notion of topological compactness, finite closed intervals and topological compactness.
