. . "RIV/47813059:19610/10:#0000267!RIV10-MSM-19610___" . "The space of omega-limit sets of piecewise continuous maps of the interval"@en . "1023-6198" . . "16"^^ . "000275127200012" . "The space of omega-limit sets of piecewise continuous maps of the interval"@en . . "Hofbauer, Franz" . . "According to a well-known result, the collection of all omega-limit sets of a continuous map of the interval equipped with the Hausdorff metric is a compact metric space. In this paper, a similar result is proved for piecewise continuous maps with finitely many points of discontinuity, if the points of discontinuity are not periodic for any variant of the map. A variant of f is a map g coinciding with f at any point of continuity and being continuous from one side at any point of discontinuity. It is also shown that omega-limit sets of these maps are locally saturating, another property known for continuous maps. However, contrary to the situation for continuous maps, there are piecewise continuous maps having locally saturating sets which are not omega-limit sets. A condition implying that a locally saturating set is an omega-limit set is presented" . "[6A9EA48D7611]" . . . . "288928" . "19610" . . "GB - Spojen\u00E9 kr\u00E1lovstv\u00ED Velk\u00E9 Brit\u00E1nie a Severn\u00EDho Irska" . "Z(MSM4781305904)" . . . . "Sm\u00EDtal, Jaroslav" . "1"^^ . "The space of omega-limit sets of piecewise continuous maps of the interval" . . "3"^^ . "RIV/47813059:19610/10:#0000267" . "2-3" . "According to a well-known result, the collection of all omega-limit sets of a continuous map of the interval equipped with the Hausdorff metric is a compact metric space. In this paper, a similar result is proved for piecewise continuous maps with finitely many points of discontinuity, if the points of discontinuity are not periodic for any variant of the map. A variant of f is a map g coinciding with f at any point of continuity and being continuous from one side at any point of discontinuity. It is also shown that omega-limit sets of these maps are locally saturating, another property known for continuous maps. However, contrary to the situation for continuous maps, there are piecewise continuous maps having locally saturating sets which are not omega-limit sets. A condition implying that a locally saturating set is an omega-limit set is presented"@en . . . "The space of omega-limit sets of piecewise continuous maps of the interval" . "Journal of Difference Equations and Applications" . "Raith, Peter" . . "omega-limit set; Hausdorff metric; piecewise continuous map; interval map; compactness; locally saturating set"@en . . "16" . .