ABSTRACT
This chapter contains notation and definitions related to the integration theory. It recalls the De Morgan’s laws and describes the concepts of mapping functions, topological space, Hausdorff space, and pseudometric space. The mapping functions include injective mapping, surjective mapping, and bijective mapping. A pseudometric space is separable if and only if it has a countable base. Hence every subspace of a separable pseudometric space is separable. The chapter explains the Urysohn’s theorem and Tietze extension theorem. It also derives equations for Cauchy sequence, normed space, and Banach space. The space X is a Hilbert space if it is a Banach space with respect to the induced norm.
