Re: Open sets in R^n
- From: "G. A. Edgar" <edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Wed, 04 Jun 2008 07:48:17 -0400
In article <slrng4cmaf.kvf.tim@xxxxxxxxxxxxxxxxxxxxxxxxxx>, Tim Little
<tim@xxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
On 2008-06-04, Virgil <Virgil@xxxxxxxxx> wrote:
How does one cover the interior of a square in R^2 with the disjoint
interiors of countably many circles plus a set of measure zero?
The obvious sequence of circles defined by "the largest possible
circle within the remaining space" (with some rule for ties) should
cover all but a set of measure zero.
- Tim
The remainder, known as the gasket of Appolonius, has Hausdorff
dimension < 2 (in fact around 1 --- considerable calculation is
required to see it is > 1). But dimension < 2 is enough to show
Lebesgue measure zero.
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
.
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- Open sets in R^n
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- Re: Open sets in R^n
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- Re: Open sets in R^n
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- Re: Open sets in R^n
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- Open sets in R^n
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