MS-C1541 - Metric Spaces, 11.01.2021-25.02.2021
Kurssiasetusten perusteella kurssi on päättynyt 25.02.2021 Etsi kursseja: MS-C1541
Osion kuvaus
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General matters
Course arrangements
Overview of the course
Chapter I
On set theory and notation
Functions
Real number sequences
Convergence of number sequences
Axioms of real numbers
Chapter III
Subsequences of real number sequences
Continuity of functions
Chapter IV
Inner product spaces
(Zoom recording of the remaining part failed, see the lecture notes instead.)Normed spaces
(Zoom recording of the remaining part failed, see the lecture notes instead.)The sup-norm example from Lecture 5:Metric inherited by a subset of a metric space
Open and closed sets (postponed until Wednesday...)
Chapter VI
Continuity of functions between metric spaces
Lipschitz continuity and examples
Characterization of continuity
Chapter VII
Homeomorphisms
Chapter VIII
Sequences and limits in metric spaces
Characterization of closed sets and continuity using sequences
Chapter IX
Pointwise convergence and uniform convergence of function sequences
Completeness
Contraction mapping principle (Banach's fixed point theorem)