Chapter 8 begins with a detailed exposition of the usual topological notions and theorems related to them. It thoroughly explains the nonstandard version of these topological concepts and proves the theorems required for the economic theory presented in later chapters. It adds some results concerning the topology of the extensions of real vector spaces, which were discussed in Chap. 7 , such as the Heine–Borel Theorem. It then introduces nonstandard topologies and proves the relevant results concerning them for use in the subsequent chapters.