Re: Isometries of closed disks

En el mensaje: [EMAIL PROTECTED],
Jose Carlos Santos <[EMAIL PROTECTED]> dijo:
> Hi all,
>
> Each closed disk in the plane has the following properties:
>
> 1) it's compact;
>
> 2) its interior is non-empty;
>
> 3) its boundary is connected;
>
> 4) its group of isometries is infinite.
>
> My question is: are closed disks the only plane sets with these
> properties. My guess is that the answer is yes. Does anyone know
> how to prove it?

Following D. Ulrich idea, take straight segments of length 1 from origin, at
any angle that be a rational multiple of pi, from OX axis. Add a closed disk
of centre O and radius less than 1.


-- 
Best regards,

Ignacio Larrosa Cañestro
A Coruña (España)
[EMAIL PROTECTED]