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1 LIGM - Laboratoire d-Informatique Gaspard-Monge 2 LRDE - Laboratoire de Recherche et de Développement de l-EPITA

Abstract : The main question of this paper 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 maxima and minima in the same way, 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 interpret any function defined on a grid as a -continuous- function thanks to an interpolation scheme. The continuity properties are essential to obtain a quasi-linear algorithm for computing the tree of shapes in any dimension, which is exposed in a companion paper.

Keywords : T0-Alexandroff space discrete topology continuity tree of shapes





Author: Laurent Najman - Thierry Géraud -

Source: https://hal.archives-ouvertes.fr/



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