The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Lovelock and Rund: Star shaped set of points on a manifold
Replies: 7   Last Post: Jan 17, 2013 2:39 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 2,637
Registered: 1/8/12
Re: Lovelock and Rund: Star shaped set of points on a manifold
Posted: Jan 16, 2013 10:23 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Wed, 16 Jan 2013, Hetware wrote:

> "for a given point P on X_n let us choose our coordinates such that
> x^1=...=x^n=0 at P, after which we construct an open set U on X_n which is
> defined by the property that for any point Q element of U with coordinates
> x^h, the segment consisting of the points with coordinates tx^h, 0<=t<=1, is
> also contained in U."
> I'm having a bit of trouble grasping that concept. Let's take R^2, for
> example. I choose a point in the middle of my paper, and call it {0,0}. I
> now declare it to be a member of some open set U.

A star set is an open set that's radially convex.

A star set with p as it's center is an open set U with p in U
and for all x in U, the line from p to x lies within U.

> The smallest possible U is some infinitesimal open disk centered on P.

There is no smallest possible star set with p as it center
unless p is an isolated point. Infinitesimal open disks are
an allusion. Open disks with a (sufficiently) tiny radius
is what to think instead of those allusive disks.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.