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Find a star convex set that is not convex.

I already saw the answer on the internet but it is not clear to me, the answer is simply a figure:

enter image description here

I would like to know why this set is the one that serves, my intuition tells me that it is because the line segment that one two points of the star do not belong to the star but I do not know very well. Could anyone help me, please? Thank you very much...

ajotatxe
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user424241
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    Yes, this is a way to show that the figure is not convex. The simplest example that comes into my mind is the union of two linked (but not aligned) segments. – ajotatxe Dec 19 '17 at 18:15
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    Star-convex means that the segment from a fixed point $p_0$ to any arbitrary point $q$ in the space $X$ lies in $X$. Convex means that the segment from an arbitrary point $p\in X$ to any arbitrary point $q\in X$ lies in $X$. – anomaly Dec 19 '17 at 18:20
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    In general, a set $A$ is star convex if and only if there exists some family ${A_j}{j\in J}$ of convex sets such that $A=\bigcup{j\in J} A_j$ and $\bigcap_{j\in J}A_j\neq\emptyset$. That is, $A$ must be the union of convex sets with a common point. Of course, this does not imply that $A$ is not convex. – ajotatxe Dec 19 '17 at 18:22

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