Discrete Set-Valued Continuity and Interpolation
نویسندگان
چکیده
The main question of this talk is to retrieve some continuity properties on (discrete) T0-Alexandroff spaces. One possible application, which will guide us, is the construction of the so-called "tree of shapes" (intuitively, the tree of level lines). This tree, which should allow to process in the same way maxima and minima, faces quite a number of theoretical difficulties that we propose to solve using set-valued analysis in a purely discrete setting. We also propose a way to interprete any function defined on a grid as a "continuous" function thanks to an interpolation scheme. The continuity properties are essential to obtain a linear algorithm for computing the tree of shapes that we will develop in another talk. This is a joint work with Thierry Géraud.
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تاریخ انتشار 2013