IB Analysis and Topology

Notes I took for IB Analysis and Topology in the Cambridge Mathematical Tripos in 2024. Aimed at second-year undergraduates. Hopefully I can provide some inutition that might not be present elsewhere.

Surprisingly not much! Familiarity with mathematical symbols (e.g. here). Basic set theory, for example definition and results regarding function preimage (e.g. preimage of union is union of preimages). Proofs of theorems from IA Analysis I are good to know but not needed; the theorem statements themselves are useful but easily googleable.

• Example sheet questions

In definitions, the phrase that we define is highlighted like this.

Abbreviations:

• defn = definition
• iff = if and only if
• $\subset$ means the same thing as $\subseteq$ (i.e. "is a subset of, could be equal to")

[TODO]