Appendix to Volume 4

4A1
Set theory

Cardinals; closed cofinal sets and stationary sets; Δ-system
lemma; free sets; Ramsey's theorem; the Marriage Lemma again;
filters; normal ultrafilters; Ostaszewski's ♣; the size of
σ-algebras.

4A2
General topology

Glossary; general constructions; F_{σ}, G_{δ}, zero
and cozero sets; weight; countable chain condition; separation
axioms; compact and locally compact spaces; Lindelöf spaces;
Stone-Cech compactifications; uniform spaces;
first-countable, sequential, countably tight, metrizable
spaces; countable networks; second-countable spaces; separable
metrizable spaces; Polish spaces; order topologies; Vietoris and
Fell topologies.

4A3
Topological σ-algebras

Borel σ-algebras; measurable functions; hereditarily
Lindelöf spaces; second-countable spaces; Polish spaces;
ω_{1}; Baire σ-algebras; product spaces; compact
spaces; spaces of càdlàg functions; Baire-property algebras;
cylindrical σ-algebras.

4A4
Locally convex spaces

Linear topological spaces; locally convex spaces; Hahn-Banach
theorem; normed spaces; inner product spaces; max-flow min-cut
theorem.

4A5
Topological groups

Group actions; topological groups; uniformities; quotient groups;
metrizable groups.

4A6
Banach algebras

Stone-Weierstrass theorem (fourth form); multiplicative linear
functionals; spectral radius; invertible elements; exponentiation;
Arens multiplication.

4A7
`Later editions only'

Items recently interpolated into other volumes.

TeX,
PDF,
ro-PDF (results-only version).

Return to contents page.

Revised 10.1.2017