The Borsuk-Ulam Theorem and applications in Combinatorics , Geometry and Analysis

Postgraduate Thesis uoadl:2960283 244 Read counter

Unit:
Κατεύθυνση Θεωρητικά Μαθηματικά
Library of the School of Science
Deposit date:
2021-09-08
Year:
2021
Author:
Stamataki Despoina
Supervisors info:
Απόστολος Γιαννόπουλος , Καθηγητής , Τμήμα Μαθηματικών , ΕΚΠΑ
Παντελής Δοδός , Αναπληρωτής Καθηγητής , Τμήμα Μαθηματικών , ΕΚΠΑ
Ιωάννης Εμμανουήλ , Καθηγητής , Τμήμα Μαθηματικών , ΕΚΠΑ
Original Title:
Το Θεωρημα Borsuk-Ulam και εφαρμογές στη Συνδυαστική , τη Γεωμετρια και την Αναλυση
Languages:
Greek
Translated title:
The Borsuk-Ulam Theorem and applications in Combinatorics , Geometry and Analysis
Summary:
In this thesis we present the Borsuk-Ulam theorem and some of its
applications to Combinatorics, Geometry and Analysis. First we recall some
basic notions and tools from Algebraic Topology. Then we study several
equivalent forms of the Borsuk-Ulam theorem along with some of its proofs.
Finally, we present some applications such as the Ham-Sandwich Theorem,
the proof of the Knesser conjecture and Knaster's problem as well as its
relation to Dvoretzky's theorem.
Main subject category:
Science
Keywords:
Algebraic Topology, Borsuk-Ulam theorem, Tucker Lemma, Knaster problem, Knesser conjecture, Dvoretzky theorem
Index:
No
Number of index pages:
0
Contains images:
No
Number of references:
67
Number of pages:
93
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