Algebra in the Cech-Stone compactification and its applications to topological dyn...
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Ultrafilters applied to Ergodic Ramsey Theory
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| Author(s): |
José Carlos Fontanesi Kling
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2020-07-14 |
| Examining board members: |
Leandro Fiorini Aurichi;
Daniel Smania Brandão;
Lucia Renato Junqueira;
Samuel Gomes da Silva
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| Advisor: | Leandro Fiorini Aurichi |
| Abstract | |
Ultrafilters have applications in several fields of mathematics, such as Topology, Model Theory or Non-Standard Analysis. In this work it will be presented applications to Topological Dynamics and Ramsey Theory, aiming for the classical results from Ergodic Ramsey Theory. We present a self-contained introduction to the area, based mainly on the works of Neil Hindman, Dona Strauss and Vitaly Bergelson. (AU) | |
| FAPESP's process: | 18/08886-1 - Applications of ultrafilters to ergodic Ramsey theory |
| Grantee: | José Carlos Fontanesi Kling |
| Support Opportunities: | Scholarships in Brazil - Master |