Appendix to Volume 2
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.
The topology of Euclidean space
Closures; continuous functions; compact sets; open sets in R.
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.
Normed spaces; linear subspaces; Banach spaces; bounded linear operators; dual spaces; extending a linear operator from a dense subspace; normed algebras.
Linear topological spaces
Linear topological spaces; topologies defined by functionals; convex sets; completeness; weak topologies.
Factorization of matrices
Determinants; orthonormal families; T=PDQ where D is diagonal and P, Q are orthogonal.
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