Asymmetry of all countable orders of a real function (Q2277587)

This paper is connected with the notion of a local system which was introduced by B. Thomson. The authors define limit numbers (right- and left-hand) of order \(\alpha\) (where \(\alpha <\omega_ 1\), \(\omega_ 1\) is the first uncountable ordinal), and, consequently, they assume that x is a point of asymmetry of a function f of order \(\alpha\) if and only if the set of all left-hand numbers of order \(\alpha\) of f is different from the set of all right-hand numbers of order \(\alpha\) of f. The aim of this paper is to investigate the property of the family \(\{As^{\alpha}(f)\}_{1\leq \alpha <\omega_ 1},\) where \(As^{\alpha}(f)\) denotes the set of all points of asymmetry of f of order \(\alpha\).