Beiglböck, M. (2004). Filters in number theory and combinatorics [Dissertation, Technische Universität Wien]. reposiTUm. https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-12796
We are mainly concerned with certain applications of abstract topological methods to Combinatorics and Number Theory. The Stone-Cech Compactification beta S of a discrete semigroup S consists of the properly topologized set of ultrafilters on S. This structure provides surprisingly simple proofs of the Theorems of Hindman and van der Waerden. We derive new results about the algebraic structure of beta S and apply them to give different strengthenings of the Theorems mentioned above.<br />Some emphasis is put on Ramsey Theoretic results dealing with substructures of the positive integers which are large in an additive as well as in a multiplicative sense.
