Appendix to Volume 3
3A1
Set theory
Calculation of cardinalities; cofinal sets, cofinalities; notes on
the use of Zorn's Lemma; the natural numbers as finite ordinals;
lattice homomorphisms; the Marriage Lemma.
3A2
Rings
Rings; subrings, ideals, homomorphisms, quotient rings, the First
Isomorphism Theorem; products.
3A3
General topology
Hausdorff, regular, completely regular, zero-dimensional, extremally
disconnected, compact and locally compact spaces; continuous
functions; dense subsets; meager sets; Baire's theorem for locally
compact spaces; products; Tychonoff's theorem; the usual
topologies on {0,1}I, RI; cluster points of filters;
topology bases; uniform convergence of sequences of functions;
one-point compactifications; topologies defined from sequential
convergences.
3A4
Uniformities
Uniform spaces; and pseudometrics; uniform continuity; subspaces;
product uniformities; Cauchy filters and completeness; extending
uniformly continuous functions; completions.
3A5
Normed spaces
The Hahn-Banach theorem in analytic and geometric forms; cones and
convex sets; weak and weak* topologies; reflexive spaces; Uniform
Boundedness Theorem; strong operator topologies; completions;
normed algebras; compact linear operators; Hilbert spaces; bounded
sets in linear topological spaces.
3A6
Groups
Involutions; inner and outer automorphisms; normal subgroups.
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