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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 <> wrote:

>>On 2011-09-05, miki <> 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
Math Tutor on the Internet and in Central New Jersey and Manhattan

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