Re: closed set with measure zero

In article <d5taff$l21$1@xxxxxxxxxxxxxxxxxxx>,
Keith A. Lewis <klewis@xxxxxxxxxxxxxxxx> wrote:

>Side 2: The set is constructed by taking an uncountable continuum and
>subtracting a countable set of discrete points from it, which divides it
>into a countable set of, errr, "zero-length intervals" for lack of a better
>term.

Nonsense. If you remove a countable dense set from an interval of reals,
what remains is an _uncountable_ set. The connected components of this
set are single points. So you have divided it into an uncountable set
of "zero-length intervals".

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

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