Definition talk:Star Shaped Set

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This is an unfamiliar definition of "star-shaped" to me, I would use the word "symmetric" instead. My understanding of "star-shaped" is that there exists some point $x_0$ in the set such that the line segment connecting $x_0$ and any other point in the set is contained in the set. So a weakening of convex. Could anyone find a source for this usage of the word? Caliburn (talk) 15:19, 30 May 2022 (UTC)

I bring this up because I was about to create a page for "Balanced Set", but it currently redirects here, which I also understand to have a different meaning. Caliburn (talk) 15:26, 30 May 2022 (UTC)
The definition as given here is unsourced and very nearly unreferenced. Its only actual reference is to a page which itself has no reference. None of this area has been developed in any detail.
However, what you describe is Definition:Star Convex Set which on that page admits itself as being a different thing from a "star shaped set".
Unless you need the term "star shaped set" for something else, I recommend leave it well alone, but hijack "balanced" to mean the thing you were going to call balanced, so it is no longer directed to "Star Shaped Set" and stands alone as a separate definition. --prime mover (talk) 16:25, 30 May 2022 (UTC)
Fair enough, will do this. Caliburn (talk) 16:27, 30 May 2022 (UTC)