15 Nov
2008
15 Nov
'08
9:10 a.m.
On 11/15/08, rwg@sdf.lonestar.org <rwg@sdf.lonestar.org> wrote:
DanA>What I wrote was misunderstood.
Sorry about that, Dan!
(By the way, rwg, your last two sentences are quite interesting! I wonder how small, in some appropriate sense, that uncountable set
S = {x in [0,1]^n | #(finv(x)) > 1}
can be.
Rather huge. For the 2D Peano-Hilbert squarefiller, S = KxC U CxK, where C := [0,1] and K := the dyadic rationals therein, with the triply visited being the dense set KxK.
Well, that's huge in the sense that it's uncountable and dense, but it's "small" in at least two senses: It has measure 0, and it's a "meagre" set; that is, a countable union of nowhere dense sets. -- Andy.Latto@pobox.com