The aim of this thesis is to introduce the representation of Banach lattices with a strong unit by function spaces C(K) on compact topological spaces. To this end, the notion of Boolean algebra is introduced and Stone’s representation theorem is proven, which serves as a powerful tool in representation of Banach lattices. The Riesz space is defined, which is both a vector space and a lattice. After that, some basic properties of Riesz spaces are shown and the notions of the ideal, band, principal projection property, components of a positive vector and completeness are introduced. Freudenthal’s spectral theorem is stated without proof. In the end, the main theorem is proven, which states that every Banach lattice with a strong unit is Riesz isomorphic to some function space C(K).
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