Must the visibility function of an open set be continuous?
The visibility function of a set S was defined in 1972 by G. Beer. This function evaluates the Lebesgue outer measure of the star of each point of S. The continuity of this function for compact sets was studied by its creator. Recently, the present authors settled the problem of continuity in the bo...
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| Autores principales: | , , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_17835720_v77_n_p1_Losada |
| Aporte de: |
| Sumario: | The visibility function of a set S was defined in 1972 by G. Beer. This function evaluates the Lebesgue outer measure of the star of each point of S. The continuity of this function for compact sets was studied by its creator. Recently, the present authors settled the problem of continuity in the boundary of a compact set S. The question of the continuity in the case where S is an open bounded set - proposed by G. Beer - is still unsettled. We show here that the continuity of the visibility function does not depend on the boundedness of the open set S. |
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