In this thesis, we study the question when a local automorphism of continuous functions, or in general, of an operator algebra, is an automorphism. We also study the question how to write an n-disjointness preserving operator as a finite sum of orthomorphisms locally.

This thesis follows up the results of article A. Drápal a I. M. Wanless, On the number of quadratic orthomorphisms that produce maximally nonassociative quasigroups. This paper dealt with the density of maximally non-associative quasigroups of a certain cons- truction. However, certain cases had to be neglected in the calculations due to restrictive conditions. The examination of these cases is the subject of this work. It turned out that the asymptotic behavior in the general case as in the article differs from the beha- vior in cases examined in our work. In addition to the calculations themselves, the work contains a theoretical introduction with an explanation of the constructions used in the previous article, as well as our own theory necessary for our calculations. In addition, we experimentally verified our results. 1