Talk:Star domain

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 Field: Geometry


Hmmmm... I had always called this quality as radially convex. Tom Ruen 11:07, 12 February 2007 (UTC)

Hmmm, I never heard of "radially convex" before. The "star domain" (or other "star" variations) terminology is used quite a bit in literature, per google books. I did not try searching for "radially convex". Oleg Alexandrov (talk) 16:43, 12 February 2007 (UTC)
I'd never heard of a term for it before, so was my descriptive term. I used in the context of computer graphics - a radially convex polygon can be triangulated by adding a center point. I suppose another way to look at it as a one-to-one polar function. f(t)=r(t)*[cos(t),sin(t)], t=0..2π, f(0)=f(2π). Tom Ruen

The claim on this page that a star convex subset S of R^n is diffeomorphic to R^n is false so I am removing it. By [invariance of domain] the set S must be open. The claim seems plausible if openness is assumed, but I am not sure if any other assumptions are necessary. If someone can verify this, the result should go back in with the correct assumptions. —Preceding unsigned comment added by 66.30.114.220 (talk) 14:59, 5 August 2008 (UTC)

The assumptions that the set be nonempty and open are indeed necessary. According to exercise #8 in Chapter 1, Section 2 of Hirsch's Differential Topology, "Every nonempty starshaped open subset of R^n is C-infinity diffeomorphic to R^n."Mbw314 (talk) 21:42, 24 November 2008 (UTC)