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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_17835720_v77_n_p1_Losada |
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todo:paper_17835720_v77_n_p1_Losada2023-10-03T16:32:51Z Must the visibility function of an open set be continuous? Losada, M.P. Cunto, A.F. Toranzos, F.A. Visibility function Visibility in open sets 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. Fil:Toranzos, F.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_17835720_v77_n_p1_Losada |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Visibility function Visibility in open sets |
| spellingShingle |
Visibility function Visibility in open sets Losada, M.P. Cunto, A.F. Toranzos, F.A. Must the visibility function of an open set be continuous? |
| topic_facet |
Visibility function Visibility in open sets |
| description |
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. |
| format |
JOUR |
| author |
Losada, M.P. Cunto, A.F. Toranzos, F.A. |
| author_facet |
Losada, M.P. Cunto, A.F. Toranzos, F.A. |
| author_sort |
Losada, M.P. |
| title |
Must the visibility function of an open set be continuous? |
| title_short |
Must the visibility function of an open set be continuous? |
| title_full |
Must the visibility function of an open set be continuous? |
| title_fullStr |
Must the visibility function of an open set be continuous? |
| title_full_unstemmed |
Must the visibility function of an open set be continuous? |
| title_sort |
must the visibility function of an open set be continuous? |
| url |
http://hdl.handle.net/20.500.12110/paper_17835720_v77_n_p1_Losada |
| work_keys_str_mv |
AT losadamp mustthevisibilityfunctionofanopensetbecontinuous AT cuntoaf mustthevisibilityfunctionofanopensetbecontinuous AT toranzosfa mustthevisibilityfunctionofanopensetbecontinuous |
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1807319603533053952 |