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Topic: Question on piecewise continuity
Replies: 13   Last Post: Sep 8, 2011 9:29 AM

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Stephen J. Herschkorn

Posts: 2,297
Registered: 1/29/05
Re: Question on piecewise continuity
Posted: Sep 7, 2011 3:32 AM
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Butch Malahide wrote:

>On Sep 5, 10:55 pm, Tim Little <t...@little-possums.net> wrote:
>
>

>>On 2011-09-05, miki <miki.li...@gmail.com> wrote:
>>
>>

>>>My question is, Can G can be a disc (including the origin ) on R^2
>>>for example, and M is any simple continuous curve in that disc which
>>>splits the disc to half?
>>>The measure of that curve is zero on R^2 (isn't it)?
>>>
>>>

>>It is, yes.
>>
>>

>
>An arc (homeomorph of the closed unit interval) in the plane can have
>positive two-dimensional Lebesgue measure.
>
>


Can a *homeomorph* have this property? Or an image?

--
Stephen J. Herschkorn sjherschko@netscape.net
Math Tutor on the Internet and in Central New Jersey and Manhattan





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