**A**
Most of the Calculus topics from Rudin (Chapters 5-10),
fortified with 55 vitamins, minerals,
and secret herbs & spices;
and a selection of topics in Fourier analysis from Körner.

**A**
I expect so; at any rate it should be no *easier*
than Math 55a for most students.

**A**
It's in the dictionary -- once : twice : thrice :: 1 : 2 : 3.
As far as I know the sequence ``once, twice, thrice''
has no fourth term in English
(though it does have a zeroth term of sorts in ``never'').

**A**
Use \ll (and likewise \gg for >>). See
This PDF document
for an extensive list of such commands.

**A**
Yes.

**A**
See Dunford & Schwartz, *Linear Operators* I, p.274 ff.;
for one overview, see
this Web page.

(The name Cech should have a v-shaped diacritical mark
above the capital C; this can be done in LaTeX with ``\v{C}'',
but does not seem to have a standard HTML command.
The pronunciation is like the first syllable of ``Chekhov''.)

**A**
Start
here.