- #1
GreyZephyr
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Homework Statement
I am trying to work my way through Analysis on manifolds by Munkres. Question 14.5 has me stumped. Any hints on how to tackle it would be appreciated. The question is:
Find a bounded closed set in [tex]\mathbb{R}[/tex] that is not rectifiable
Homework Equations
A subset S of [tex]\mathbb{R}[/tex] is rectifiable iff S is bounded and the boundary of S has measure zero.
The boundary of an interval in [tex]\mathbb{R}[/tex] has measure zero.
The Attempt at a Solution
I think I need a closed set who's boundary does not have measure zero. I presume it has to be an uncountable union of intervals of some description, but I have no idea how to approach the construction of such a thing.