# Math 432: Set Theory and Topology

## Class info

• Lecture: TueThu 2–3:20pm in 2 Illini Hall
• Deconfusion session: Tue 5–5:50pm in 1 Illini Hall

## Instructor info

• Name: Anush Tserunyan
• Email: anush at illinois dot edu
• Office: 369 Altgeld Hall

## Exams

• Midterm 1: Feb 14 (Thu), 2–3:20pm in 2 Illini Hall
• Midterm 2: Mar 28 (Thu), 2–3:20pm in 2 Illini Hall
• Final exam: May 7 (Tue), 1:30–4:30pm in 2 Illini Hall

## Midterm 1

• Coverage: sets, set operations, relations, functions, partial orderings, equivalence relations, formal language and formulas, ZFC axioms, well orderings.
• What to read: Kaplansky's Sections 1.1–1.5 except for lattices in 1.3 and Sections 1–2 of my basic set theory notes [pdf].
• Practice problems: pdf

## Course material

• Textbook: Kaplansky I, Set Theory and Metric Spaces, Second Edition, AMS Chelsea Publishing, 1957
• Additional notes: A. Tserunyan, A quick introduction to basic set theory [pdf]
• What will be covered:
• Informal/naïve set theory: sets, set operations, functions
• The Zermelo–Fraenkel (ZF) axioms
• Well-orderings and ordinals
• Transfinite induction
• The set of natural numbers
• Equinumerosity: finite/infinite sets, cardinals and cardinality
• The Axiom of Choice and equivalent statements
• Introduction of reals via Dedekind cuts
• Metric spaces: examples (including the Cantor space), open/closed sets, sequences, compactness, (uniform) continuity, completion
• General topological spaces

## Homework

Only stapled homework will be accepted. Electronic copies are generally not accepted unless the student cannot make it to class for an excusable reason, which is approved by the instructor in advance.
• When is it due? Homework will be assigned each week and collected usually on Thursday in class before the lecture starts.
• Will late homework be accepted? No. To deal with contingencies, the lowest homework score will be dropped (won't count towards the total homework percentage).
• Can we work in groups? Yes, in fact, it is encouraged! But, after a group discussion of solutions to the homework exercises, each student has to write them on his/her own in his/her own words. If two solutions are too similar, they will be discarded.
• Homework format: Every homework assignment will consist of exercises from the textbook as well as not from the textbook (both equally mandatory).