Lectures: Mi 9:15-10:45, SG 3-13
Requirement: Analysis I
The following topics will be covered, among others: basic constructions, convergence (using nets and filters) and continuity, separation axioms, metrizability, compactness (compactness via open covers versus sequential compactness and countable compactness, Tichonoff's theorem), compactifications (Alexandroff and Stone-Čech compactification), the space βN, continuous functions (Urysohn's lemma, Tietze-Urysohn theorem, partitions of unity), Baire spaces.
Schedule
26.5. (Di) 13:15-14:45 (S 015): "Baire spaces and topological games" (Matthes Debes*, Marvin Polster*)
27.5. (Mi) 13:15-14:45 (S 110): "A typical continuous function is nowhere differentiable" (Leon-Emilio Erinsk*) and "Hopf fibration" (Simon Schmitt*)
15:15-16:45 (S 110): "Tychonoff's theorem" (Jakob Linnemann, Christina Wiehler)
09.6. (Di) 13:15-14:45 (S 015): "Ultrafilters as a topological space and the Stone-Cech compactification" (Hazel Rosengrün*, Manuel Westphal*)
10.6. (Mi) 13:15-14:45 (S 015): "Algebraic structure of filters and ultrafilters" (Ben Duyster*) and "Structure of semitopological semigroups" (Ann-Kristin Habermann)
23.6. (Di) 13:15-14:45 (S 015): "Applications of ultrafilters to faire voting" (Bruno Nitsch) and "Ramsey's theorem on colouring of graphs" (Minahil Zaidi*)
30.6. (Di) 13:15-14:45 (S 015): "Hindman's theorem via ultrafilters" (Rudolf Braun*) and "Van der Waerden's theorem via ultrafilters" (Benjamin Piesbergen)
* = talk in English
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