In Euclidean space, the rectangles are closed under intersection but not closed under negation/complement. I was wondering whether we can define a rectangle in an unit sphere such that the spherical rectangle is closed under intersection and/or complement.
The standard defintion of spherical rectangle: a spherical rectangle is a figure whose four edges are great circle arcs which meet at equal angles greater than 90°. Opposite arcs are equal in length. However, this is not enough to satisfy the requeirement of closed under intersection and/or complement. I was wondering whether there are some ways to restrict the spherical rectangle, e.g. enforcing them to be aligned with axis like in Euclidean space.
Is there anyway to formulate a rectangle in the sphere such that it is closed under intersection and/or complement?