Contents of Measure Theory, by D.H.Fremlin

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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Revised 24.5.11