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 (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)

Is the set of vantage points in a star domain itself convex? It seems that way in two dimensions; how about higher dimensions? 2001:14BB:140:1991:A891:A7AF:4DCE:5760 (talk) 15:05, 1 November 2015 (UTC)