A Lattice-Theoretical Shape Concept

Imre Bálint,^1,2,3 András Kocsor⁴

¹ Department of Theoretical Physics, University of Szeged,
H-6720, Szeged, Tisza L. krt. 80-82., Hungary
² Department of Pharmaceutical Analysis, University of Szeged,
H-6720, Szeged, Somogyi Béla u. 4., Hungary
³ Department of Natural Sciences, Polytechnic of the Technical University of Miskolc,
H-2400, Dunaújváros, Táncsics M. u. 1. , Hungary

⁴ Research Group on Artificial Intelligence, University of Szeged,
H-6720, Szeged, Aradi vértanúk tere 1., Hungary

Motivation. This report is on the lattice-theoretical characterization of the ‘shape’ of topological sets. The reported procedure is abstract enough to have a wide area of applications in those fields, where the classification relies on ‘similarity’ or ‘neighborhoodness’. A possible huge field is the searching for molecules with predetermined pharmacological properties. The targets of comparison can be the various type electron densities of the interacting molecular systems, when the procedure is able to give a hierarchically ordered set of more and more detailed shape characterizations, a distance concept and topology. Actually the shapes of continuous n-variable functions are investigated and the electron densities are chosen for representatives of this class, but instead of real-life computations an easy to grasp artificial example is given.