Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
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
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
