Peter Krautzberger on the web

Red workbook, p3


red workbook, p3
Red Workbook, p.3


partial translation


The talk/lecture from the previous page continues, tackling proximality with its basic characterization in terms of \beta S and starting the proof of the characterization of uniform recurrence. That’s fairly basic stuff (in the sense of necessary knowledge, not “trivial” or “easy”). The notes are a bit incomplete overall – not sure if I was too lazy (likely) or if Sabine Koppelberg jumped a bit to get to the interesting bits.

The proof that begins at the bottom of the page is, for me, a typical cases of a proof that prevents one from learning; a picture perfect proof that throws elegant arguments around but keeps from its reader the beautiful messiness of coming up with it in the first place.

The reference [HS 4.39] is alomst certainly whatever is numbered 4.39 in Hindman & Strauss, “Algebra in the Stone–Čech compactification”. (I can’t check the actual detail since my copy of H&S is still on route from LA.)

I forgot to mention in the first post that I substituted \mathfrak for Sutterlin in the transcription – Sutterlin is too hard to come by (Sutterlin U is used to indicate the neighborhood filter).