Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Supervisors info:
Β.Φαρμάκη Καθηγήτρια ΕΚΠΑ (Επιβλέπουσα), Α.Τσαρπαλιάς, Καθηγητής ΕΚΠΑ, Ν.Παπαναστασίου Αναπλ. Καθηγητής ΕΚΠΑ
Original Title:
Το απειροσυνδυαστικό θεώρημα του Hindman και οι επεκτάσεις του
Translated title:
The infinity-combined Hindman’s theorem and its extensions
Summary:
In this thesis a first step we do a flashback in Ramsey Theory and record a
short proof of Hindman’s Theorem belonging to J.Baumgartner. Then, we prove a
general theorem of Hindman’s Theorem for semigroups relying on Theory of
ultrafilters.
Thus, in the next step we develop the theory of semigroups and their ideals.
Then, putting the semigroup and write a topology returns on the right
topological semigroups. Next, we define the space of ultrafilters, first a
discrete space and after a semigroup and talking to Stone-Cech compactification
initially a discrete space and after a semigroup. We conclude with some
applications of the Theory of Ramsey.
Keywords:
Hindman’s theorem, -Cech compactification, Semigroups, Idempotents, Ultrafilters
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