Appendix to Volume 2
2A1
Set theory
Ordered sets; transfinite recursion; ordinals; initial ordinals;
Schröder-Bernstein theorem; filters; Axiom of Choice;
Zermelo's Well-Ordering Theorem; Zorn's Lemma; ultrafilters; a
theorem in combinatorics.
2A2
The topology of Euclidean space
Closures; continuous functions; compact sets; open sets in
R.
2A3
General topology
Topologies; continuous functions; subspace topologies; closures and
interiors; Hausdorff topologies; pseudometrics; convergence of
sequences; compact spaces; cluster points of sequences; convergence
of filters; lim sup and lim inf; product topologies; dense subsets.
2A4
Normed spaces
Normed spaces; linear subspaces; Banach spaces; bounded linear
operators; dual spaces; extending a linear operator from a dense
subspace; normed algebras.
2A5
Linear topological spaces
Linear topological spaces; topologies defined by functionals; convex
sets; completeness; weak topologies.
2A6
Factorization of matrices
Determinants; orthonormal families; T=PDQ where D is diagonal
and P, Q are orthogonal.
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