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Let $\Omega$ be a bounded domain (open connected) in the Euclidean space, that contains the origin. Is there a name/what can I call for the cone like region with tip at the origin and base at some portion of the boundary ?

It looks like what one sees when hold a flash light at the origin and there is a light spot on the "wall= a portion of the boundary ".

What if $\Omega$ is a ball, does that region have a particular name in this case? Thanks

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    $\begingroup$ Something like a sector? There are also spherical sectors. Maybe you can appropriately generalize the term for your purpose, e.g. as the intersection of a cone and your domain. $\endgroup$ – M. Winter Jan 12 '18 at 14:07
  • $\begingroup$ A picture would be helpful, but "sector" seems to capture the idea pretty well. $\endgroup$ – Xander Henderson Jan 12 '18 at 14:27
  • $\begingroup$ The thing is the light spot is not regularly shaped because the boundary is not normally, but connected however. It I looked up the spherical sector it seems correct in case of balls except for that it is used for that part of the sphere not the cone we are talking about here. $\endgroup$ – Medo Jan 12 '18 at 14:30

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