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Topic: Equidistance
Replies: 7   Last Post: Jul 13, 2013 12:22 AM

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William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Equidistance
Posted: Jul 13, 2013 12:22 AM
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On Fri, 12 Jul 2013, quasi wrote:
> William Elliot wrote:

> >Let (S,d) be a compact Hausdorff space and f:S -> S a
> >homeomorphism. How can it be show that there are some distinct
> >x and y for which d(f(x),f(y)) = d(x,y)?

> Presumably you meant compact _metric_ space.
> Still, I don't believe the claim.

Me neither. I left out an important premise.
Let p1,.. pj be j consequitive points on a circle for which
d(p1,p2),.. d(p_(j-1),pj), d(pj,p1) are all different and
rotate the points, p1 -> p2,.. p_(j-1) -> pj, pj -> p1.

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