Abstract
This paper investigates algebraic and continuity properties of increasing set operators underlying dynamic systems. We recall algebraic properties of increasing operators on complete lattices and some topologies used for the study of continuity properties of lattice operators. We apply these notions to several operators induced by a differential equation or differential inclusion. We especially focus on the operators associating with any closed subset its reachable set, its exit tube, its viability kernel or its invariance kernel. Finally, we show that morphological operators used in image processing are particular cases of operators induced by constant differential inclusion.
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Mattioli, J., Doyen, L. & Najman, L. Lattice operators underlying dynamic systems. Set-Valued Anal 4, 119–134 (1996). https://doi.org/10.1007/BF00425961
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DOI: https://doi.org/10.1007/BF00425961