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Topic:
Subset of the square
Replies:
9
Last Post:
Nov 25, 2000 12:55 PM




Re: Subset of the square
Posted:
Nov 23, 2000 8:37 PM


Colin Hayman wrote: > > > Joseph levine wrote: > > > Does there exist a subset of the unit square such that all horizontal > > > lines intersect the set in countably many points but all vertical > > > lines intersect the set in uncountably many points? > > > > ((x, y): x rational, 0 < x,y < 1) would seem to be a trivial solution. > > That was one of my first thoughts, but consider the vertical line x = > 1/pi. Any point on that line has an irrational xcoordinate between 0 and > 1 (namely 1/pi), so it doesn't contain any points from your subset  and > zero is about as countable as it gets.
Thanks, I suspected I had to be missing something.
Hugo



