The infinity-combined Hindman’s theorem and its extensions

Postgraduate Thesis uoadl:1320417 778 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2014-10-30
Year:
2014
Author:
Λωρίδα Πηνελόπη
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
Languages:
Greek
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
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
40
Number of pages:
126
File:
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